Find if a list is an ABC-triple

Three positive integers A, B, C are ABC-triple if they are coprime,
with A < B and satisfying the relation : A + B = C

Examples :

1, 8, 9 is an ABC-triple since they are coprime, 1 < 8 and 1 + 8 = 9

6, 8, 14 is not because they are not coprime

7, 5, 12 is not because 7 > 5

You can see this Frits Beukers 2005 presentation for more details about ABC-triples.

Input/Output

Three integers, decimal written. May be separated values or
list. Output had to be a truthy/falsy value whether the three
integers are an ABC-triple.

Test cases

Each of the following lists should output a truthy value

[1, 8, 9]

[2, 3, 5]

[2, 6436341, 6436343]

[4, 121, 125]

[121, 48234375, 48234496]

Each of the following lists should output a falsy value

[1, 1, 2]

[1, 2, 5]

[1, 9, 8]

[4, 12872682, 12872686]

[6, 8, 14]

[7, 5, 12]

Rules

No particular rules!

edited 1 hour ago

Luis Mendo

74k886291

asked 1 hour ago

david

16919

Does the output have to be only one of two values, or can we output different truthy/falsy values for different inputs?
– Luis Mendo
1 hour ago

I think it should be consistent: your code have to output one kind of truthy/falsy values whatever the input. But the truthy/falsy couple can be what you want as far as it does the job: differentiate lists.
– david
1 hour ago

If we take the input as list of three values, does the input have to be in the order [A,B,C], or are we also allowed to take the input in the order [C,B,A] or [C,A,B]?
– Kevin Cruijssen
39 mins ago

You have to respect order since A < B is a criteria in the challenge.
– david
37 mins ago

@david A < B can still be respected when we take the input list in the order [C,A,B]. ;) But ok, perhaps it's indeed best to leave the input-order for lists-input as [A,B,C] to reduce confusion.
– Kevin Cruijssen
33 mins ago

|
show 1 more comment

Three positive integers A, B, C are ABC-triple if they are coprime,
with A < B and satisfying the relation : A + B = C

Examples :

1, 8, 9 is an ABC-triple since they are coprime, 1 < 8 and 1 + 8 = 9

6, 8, 14 is not because they are not coprime

7, 5, 12 is not because 7 > 5

You can see this Frits Beukers 2005 presentation for more details about ABC-triples.

Input/Output

Three integers, decimal written. May be separated values or
list. Output had to be a truthy/falsy value whether the three
integers are an ABC-triple.

Test cases

Each of the following lists should output a truthy value

[1, 8, 9]

[2, 3, 5]

[2, 6436341, 6436343]

[4, 121, 125]

[121, 48234375, 48234496]

Each of the following lists should output a falsy value

[1, 1, 2]

[1, 2, 5]

[1, 9, 8]

[4, 12872682, 12872686]

[6, 8, 14]

[7, 5, 12]

Rules

No particular rules!

edited 1 hour ago

Luis Mendo

74k886291

asked 1 hour ago

david

16919

Does the output have to be only one of two values, or can we output different truthy/falsy values for different inputs?
– Luis Mendo
1 hour ago

I think it should be consistent: your code have to output one kind of truthy/falsy values whatever the input. But the truthy/falsy couple can be what you want as far as it does the job: differentiate lists.
– david
1 hour ago

If we take the input as list of three values, does the input have to be in the order [A,B,C], or are we also allowed to take the input in the order [C,B,A] or [C,A,B]?
– Kevin Cruijssen
39 mins ago

You have to respect order since A < B is a criteria in the challenge.
– david
37 mins ago

@david A < B can still be respected when we take the input list in the order [C,A,B]. ;) But ok, perhaps it's indeed best to leave the input-order for lists-input as [A,B,C] to reduce confusion.
– Kevin Cruijssen
33 mins ago

|
show 1 more comment

Three positive integers A, B, C are ABC-triple if they are coprime,
with A < B and satisfying the relation : A + B = C

Examples :

1, 8, 9 is an ABC-triple since they are coprime, 1 < 8 and 1 + 8 = 9

6, 8, 14 is not because they are not coprime

7, 5, 12 is not because 7 > 5

You can see this Frits Beukers 2005 presentation for more details about ABC-triples.

Input/Output

Three integers, decimal written. May be separated values or
list. Output had to be a truthy/falsy value whether the three
integers are an ABC-triple.

Test cases

Each of the following lists should output a truthy value

[1, 8, 9]

[2, 3, 5]

[2, 6436341, 6436343]

[4, 121, 125]

[121, 48234375, 48234496]

Each of the following lists should output a falsy value

[1, 1, 2]

[1, 2, 5]

[1, 9, 8]

[4, 12872682, 12872686]

[6, 8, 14]

[7, 5, 12]

Rules

No particular rules!

edited 1 hour ago

Luis Mendo

74k886291

asked 1 hour ago

david

16919

Three positive integers A, B, C are ABC-triple if they are coprime,
with A < B and satisfying the relation : A + B = C

Examples :

1, 8, 9 is an ABC-triple since they are coprime, 1 < 8 and 1 + 8 = 9

6, 8, 14 is not because they are not coprime

7, 5, 12 is not because 7 > 5

You can see this Frits Beukers 2005 presentation for more details about ABC-triples.

Input/Output

Three integers, decimal written. May be separated values or
list. Output had to be a truthy/falsy value whether the three
integers are an ABC-triple.

Test cases

Each of the following lists should output a truthy value

[1, 8, 9]

[2, 3, 5]

[2, 6436341, 6436343]

[4, 121, 125]

[121, 48234375, 48234496]

Each of the following lists should output a falsy value

[1, 1, 2]

[1, 2, 5]

[1, 9, 8]

[4, 12872682, 12872686]

[6, 8, 14]

[7, 5, 12]

Rules

No particular rules!

code-golf sequence decision-problem number-theory

edited 1 hour ago

Luis Mendo

74k886291

asked 1 hour ago

david

16919

edited 1 hour ago

Luis Mendo

74k886291

asked 1 hour ago

david

16919

edited 1 hour ago

Luis Mendo

74k886291

edited 1 hour ago

Luis Mendo

74k886291

edited 1 hour ago

Luis Mendo

74k886291

asked 1 hour ago

david

16919

asked 1 hour ago

david

16919

asked 1 hour ago

david

16919

Does the output have to be only one of two values, or can we output different truthy/falsy values for different inputs?
– Luis Mendo
1 hour ago

I think it should be consistent: your code have to output one kind of truthy/falsy values whatever the input. But the truthy/falsy couple can be what you want as far as it does the job: differentiate lists.
– david
1 hour ago

If we take the input as list of three values, does the input have to be in the order [A,B,C], or are we also allowed to take the input in the order [C,B,A] or [C,A,B]?
– Kevin Cruijssen
39 mins ago

You have to respect order since A < B is a criteria in the challenge.
– david
37 mins ago

@david A < B can still be respected when we take the input list in the order [C,A,B]. ;) But ok, perhaps it's indeed best to leave the input-order for lists-input as [A,B,C] to reduce confusion.
– Kevin Cruijssen
33 mins ago

|
show 1 more comment

Does the output have to be only one of two values, or can we output different truthy/falsy values for different inputs?
– Luis Mendo
1 hour ago

I think it should be consistent: your code have to output one kind of truthy/falsy values whatever the input. But the truthy/falsy couple can be what you want as far as it does the job: differentiate lists.
– david
1 hour ago

If we take the input as list of three values, does the input have to be in the order [A,B,C], or are we also allowed to take the input in the order [C,B,A] or [C,A,B]?
– Kevin Cruijssen
39 mins ago

You have to respect order since A < B is a criteria in the challenge.
– david
37 mins ago

@david A < B can still be respected when we take the input list in the order [C,A,B]. ;) But ok, perhaps it's indeed best to leave the input-order for lists-input as [A,B,C] to reduce confusion.
– Kevin Cruijssen
33 mins ago

Does the output have to be only one of two values, or can we output different truthy/falsy values for different inputs?
– Luis Mendo
1 hour ago

I think it should be consistent: your code have to output one kind of truthy/falsy values whatever the input. But the truthy/falsy couple can be what you want as far as it does the job: differentiate lists.
– david
1 hour ago

If we take the input as list of three values, does the input have to be in the order [A,B,C], or are we also allowed to take the input in the order [C,B,A] or [C,A,B]?
– Kevin Cruijssen
39 mins ago

You have to respect order since A < B is a criteria in the challenge.
– david
37 mins ago

@david A < B can still be respected when we take the input list in the order [C,A,B]. ;) But ok, perhaps it's indeed best to leave the input-order for lists-input as [A,B,C] to reduce confusion.
– Kevin Cruijssen
33 mins ago

|
show 1 more comment

8 Answers
8

active

oldest

votes

Perl 6, 33 bytes

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

Try it online!

Anonymous code block that takes a list of three numbers and returns True or False.

Explanation

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

{                               }  # Anonymous code block

                        [gcd] $_   # Is the gcd of all the numbers

 (                   )==           # Equal to

  .sum         # Whether the sum of numbes

      ==       # Is equal to

        .[2]*2 # The last element doubled

              *[<] $_   # And elements are in ascending order

edited 1 hour ago

answered 1 hour ago

Jo King

20.8k247110

32 bytes
– nwellnhof
36 mins ago

add a comment |

05AB1E, 12 11 bytes

`‹sÂÆ_s¿PΘ

Try it online!
or as a Test Suite

Explanation

`            # push values of input list separately to stack

            # remove the top (last) value

  ‹          # is a < b ?

   sÂÆ       # reduce a reversed copy of the input by subtraction

      _      # logically negate

       s¿    # push the gcd of the input

         P   # product of the stack

          Θ  # is true ?

edited 52 mins ago

answered 1 hour ago

Emigna

45.4k432138

Nice answer! I like the reduce by subtraction on the reversed input RÆ you've used to check if A + B = C. Too bad there isn't an "are all values on the stack equal" single-byte builtin (we can use )Ë of course, but it's just as long as PΘ). I've asked OP if it's allowed to take the input in the order [C,B,A], in which case it can be 10 bytes like this: ¦`›sÆ_I¿PΘ.
– Kevin Cruijssen
35 mins ago

add a comment |

Python 2, 69 67 63 62 bytes

lambda a,b,c:(c-b==a<b)/gcd(gcd(a,b),c)

from fractions import*

Try it online!

Python 3, 58 bytes

lambda a,b,c:(c-b==a<b)==gcd(gcd(a,b),c)

from math import*

Try it online!

edited 49 mins ago

answered 1 hour ago

TFeld

14.2k21240

is the gcd in gcd trick valid? What if a is not coprime with c?
– Jo King
1 hour ago

2

@jo-king If p divides a and c, it should divide c-a so b.
– david
1 hour ago

2

@JoKing: It is in this case, but not in general (you can prove it via Bezout's identity).
– BMO
1 hour ago

add a comment |

JavaScript (ES6), 54 bytes

Returns $0$ or $1$.

(a,b,c)=>(g=(x,y=a)=>y?g(y,x%y):x)(b)*g(c)==a<b&a+b==c

Try it online!

How?

The helper function $g(x)$ computes the GCD of $x$ and $a$. To test whether $a$, $b$ and $c$ are coprime, we test whether $g(b)g(c)=1$. The right part of the equality is replaced with the result of the condition $a<b$.

edited 40 mins ago

answered 1 hour ago

Arnauld

72.4k689305

add a comment |

Haskell, 48 38 bytes

^{-10 bytes due to TFeld's gcd trick!}

g [a,b,c]=a<b&&a+b==c&&gcd(gcd a b)c<2

Try it online!

Explanation

The first two conditions a < b and a + b == c are obvious, the third uses TFeld's intuition:

Let us write $d = gcd(a,b)$. With Bézout's identity we can write $d = U cdot a + V cdot b$ and similarly $e = gcd(d,c) = X cdot d + Y cdot c$.

Since we know that $a + b = c$ we can substitute $c$ and $b$ in the above identities, yielding two equations only in $a,b$ and $a,c$ respectively. Since the $gcd$ is the smallest positive element satisfying Bézout's identity the above condition is sufficient.

edited 39 mins ago

answered 1 hour ago

BMO

11.5k22186

add a comment |

Jelly, 10 7 bytes

:<ƝḋgƝe

Try it online!

How it works

:<ƝḋgƝe  Main link. Argument: [a, b, c] (positive integers)



 <Ɲ      Less than neighbors; yield [(a < b), (b < c)].

:        Integer division; yield [a : (a < b), b : (b < c), c].

         The quotient is +oo if the divisor is 0.

    gƝ   GCD neighbors; yield [gcd(a, b), gcd(b, c)].

   ḋ     Dot product; yield (a : (a < b) × gcd(a, b) + b : (b < c) × gcd(b, c)).

      e  Check if the result exists in [a, b, c].

edited 5 mins ago

answered 25 mins ago

Dennis♦

186k32296735

add a comment |

Japt, 16 14 bytes

<V&Näj ×&U+V¥W

Try it

edited 56 mins ago

answered 1 hour ago

Shaggy

18.9k21666

add a comment |

J, 27 bytes

(+/=2*{:)*({.<1{])*1=+./ .*

Try it online!

Inspired by Jo King's Perl solution

edited 31 mins ago

answered 38 mins ago

Galen Ivanov

6,34711032

add a comment |

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8 Answers
8

active

oldest

votes

8 Answers
8

active

oldest

votes

Perl 6, 33 bytes

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

Try it online!

Anonymous code block that takes a list of three numbers and returns True or False.

Explanation

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

{                               }  # Anonymous code block

                        [gcd] $_   # Is the gcd of all the numbers

 (                   )==           # Equal to

  .sum         # Whether the sum of numbes

      ==       # Is equal to

        .[2]*2 # The last element doubled

              *[<] $_   # And elements are in ascending order

edited 1 hour ago

answered 1 hour ago

Jo King

20.8k247110

32 bytes
– nwellnhof
36 mins ago

add a comment |

Perl 6, 33 bytes

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

Try it online!

Anonymous code block that takes a list of three numbers and returns True or False.

Explanation

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

{                               }  # Anonymous code block

                        [gcd] $_   # Is the gcd of all the numbers

 (                   )==           # Equal to

  .sum         # Whether the sum of numbes

      ==       # Is equal to

        .[2]*2 # The last element doubled

              *[<] $_   # And elements are in ascending order

edited 1 hour ago

answered 1 hour ago

Jo King

20.8k247110

32 bytes
– nwellnhof
36 mins ago

add a comment |

Perl 6, 33 bytes

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

Try it online!

Anonymous code block that takes a list of three numbers and returns True or False.

Explanation

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

{                               }  # Anonymous code block

                        [gcd] $_   # Is the gcd of all the numbers

 (                   )==           # Equal to

  .sum         # Whether the sum of numbes

      ==       # Is equal to

        .[2]*2 # The last element doubled

              *[<] $_   # And elements are in ascending order

edited 1 hour ago

answered 1 hour ago

Jo King

20.8k247110

Perl 6, 33 bytes

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

Try it online!

Anonymous code block that takes a list of three numbers and returns True or False.

Explanation

{(.sum==.[2]*2*[<] $_)==[gcd] $_}

{                               }  # Anonymous code block

                        [gcd] $_   # Is the gcd of all the numbers

 (                   )==           # Equal to

  .sum         # Whether the sum of numbes

      ==       # Is equal to

        .[2]*2 # The last element doubled

              *[<] $_   # And elements are in ascending order

edited 1 hour ago

answered 1 hour ago

Jo King

20.8k247110

edited 1 hour ago

answered 1 hour ago

Jo King

20.8k247110

answered 1 hour ago

Jo King

20.8k247110

answered 1 hour ago

Jo King

20.8k247110

32 bytes
– nwellnhof
36 mins ago

add a comment |

32 bytes
– nwellnhof
36 mins ago

32 bytes
– nwellnhof
36 mins ago

add a comment |

05AB1E, 12 11 bytes

`‹sÂÆ_s¿PΘ

Try it online!
or as a Test Suite

Explanation

`            # push values of input list separately to stack

            # remove the top (last) value

  ‹          # is a < b ?

   sÂÆ       # reduce a reversed copy of the input by subtraction

      _      # logically negate

       s¿    # push the gcd of the input

         P   # product of the stack

          Θ  # is true ?

edited 52 mins ago

answered 1 hour ago

Emigna

45.4k432138

Nice answer! I like the reduce by subtraction on the reversed input RÆ you've used to check if A + B = C. Too bad there isn't an "are all values on the stack equal" single-byte builtin (we can use )Ë of course, but it's just as long as PΘ). I've asked OP if it's allowed to take the input in the order [C,B,A], in which case it can be 10 bytes like this: ¦`›sÆ_I¿PΘ.
– Kevin Cruijssen
35 mins ago

add a comment |

05AB1E, 12 11 bytes

`‹sÂÆ_s¿PΘ

Try it online!
or as a Test Suite

Explanation

`            # push values of input list separately to stack

            # remove the top (last) value

  ‹          # is a < b ?

   sÂÆ       # reduce a reversed copy of the input by subtraction

      _      # logically negate

       s¿    # push the gcd of the input

         P   # product of the stack

          Θ  # is true ?

edited 52 mins ago

answered 1 hour ago

Emigna

45.4k432138

Nice answer! I like the reduce by subtraction on the reversed input RÆ you've used to check if A + B = C. Too bad there isn't an "are all values on the stack equal" single-byte builtin (we can use )Ë of course, but it's just as long as PΘ). I've asked OP if it's allowed to take the input in the order [C,B,A], in which case it can be 10 bytes like this: ¦`›sÆ_I¿PΘ.
– Kevin Cruijssen
35 mins ago

add a comment |

05AB1E, 12 11 bytes

`‹sÂÆ_s¿PΘ

Try it online!
or as a Test Suite

Explanation

`            # push values of input list separately to stack

            # remove the top (last) value

  ‹          # is a < b ?

   sÂÆ       # reduce a reversed copy of the input by subtraction

      _      # logically negate

       s¿    # push the gcd of the input

         P   # product of the stack

          Θ  # is true ?

edited 52 mins ago

answered 1 hour ago

Emigna

45.4k432138

05AB1E, 12 11 bytes

`‹sÂÆ_s¿PΘ

Try it online!
or as a Test Suite

Explanation

`            # push values of input list separately to stack

            # remove the top (last) value

  ‹          # is a < b ?

   sÂÆ       # reduce a reversed copy of the input by subtraction

      _      # logically negate

       s¿    # push the gcd of the input

         P   # product of the stack

          Θ  # is true ?

edited 52 mins ago

answered 1 hour ago

Emigna

45.4k432138

edited 52 mins ago

answered 1 hour ago

Emigna

45.4k432138

answered 1 hour ago

Emigna

45.4k432138

answered 1 hour ago

Emigna

45.4k432138

Nice answer! I like the reduce by subtraction on the reversed input RÆ you've used to check if A + B = C. Too bad there isn't an "are all values on the stack equal" single-byte builtin (we can use )Ë of course, but it's just as long as PΘ). I've asked OP if it's allowed to take the input in the order [C,B,A], in which case it can be 10 bytes like this: ¦`›sÆ_I¿PΘ.
– Kevin Cruijssen
35 mins ago

add a comment |

Nice answer! I like the reduce by subtraction on the reversed input RÆ you've used to check if A + B = C. Too bad there isn't an "are all values on the stack equal" single-byte builtin (we can use )Ë of course, but it's just as long as PΘ). I've asked OP if it's allowed to take the input in the order [C,B,A], in which case it can be 10 bytes like this: ¦`›sÆ_I¿PΘ.
– Kevin Cruijssen
35 mins ago

Nice answer! I like the reduce by subtraction on the reversed input RÆ you've used to check if A + B = C. Too bad there isn't an "are all values on the stack equal" single-byte builtin (we can use )Ë of course, but it's just as long as PΘ). I've asked OP if it's allowed to take the input in the order [C,B,A], in which case it can be 10 bytes like this: ¦`›sÆ_I¿PΘ.
– Kevin Cruijssen
35 mins ago

add a comment |

Python 2, 69 67 63 62 bytes

lambda a,b,c:(c-b==a<b)/gcd(gcd(a,b),c)

from fractions import*

Try it online!

Python 3, 58 bytes

lambda a,b,c:(c-b==a<b)==gcd(gcd(a,b),c)

from math import*

Try it online!

edited 49 mins ago

answered 1 hour ago

TFeld

14.2k21240

is the gcd in gcd trick valid? What if a is not coprime with c?
– Jo King
1 hour ago

2

@jo-king If p divides a and c, it should divide c-a so b.
– david
1 hour ago

2

@JoKing: It is in this case, but not in general (you can prove it via Bezout's identity).
– BMO
1 hour ago

add a comment |

Python 2, 69 67 63 62 bytes

lambda a,b,c:(c-b==a<b)/gcd(gcd(a,b),c)

from fractions import*

Try it online!

Python 3, 58 bytes

lambda a,b,c:(c-b==a<b)==gcd(gcd(a,b),c)

from math import*

Try it online!

edited 49 mins ago

answered 1 hour ago

TFeld

14.2k21240

is the gcd in gcd trick valid? What if a is not coprime with c?
– Jo King
1 hour ago

2

@jo-king If p divides a and c, it should divide c-a so b.
– david
1 hour ago

2

@JoKing: It is in this case, but not in general (you can prove it via Bezout's identity).
– BMO
1 hour ago

add a comment |

Python 2, 69 67 63 62 bytes

lambda a,b,c:(c-b==a<b)/gcd(gcd(a,b),c)

from fractions import*

Try it online!

Python 3, 58 bytes

lambda a,b,c:(c-b==a<b)==gcd(gcd(a,b),c)

from math import*

Try it online!

edited 49 mins ago

answered 1 hour ago

TFeld

14.2k21240

Python 2, 69 67 63 62 bytes

lambda a,b,c:(c-b==a<b)/gcd(gcd(a,b),c)

from fractions import*

Try it online!

Python 3, 58 bytes

lambda a,b,c:(c-b==a<b)==gcd(gcd(a,b),c)

from math import*

Try it online!

edited 49 mins ago

answered 1 hour ago

TFeld

14.2k21240

edited 49 mins ago

answered 1 hour ago

TFeld

14.2k21240

answered 1 hour ago

TFeld

14.2k21240

answered 1 hour ago

TFeld

14.2k21240

is the gcd in gcd trick valid? What if a is not coprime with c?
– Jo King
1 hour ago

2

@jo-king If p divides a and c, it should divide c-a so b.
– david
1 hour ago

2

@JoKing: It is in this case, but not in general (you can prove it via Bezout's identity).
– BMO
1 hour ago

add a comment |

is the gcd in gcd trick valid? What if a is not coprime with c?
– Jo King
1 hour ago

2

@jo-king If p divides a and c, it should divide c-a so b.
– david
1 hour ago

2

@JoKing: It is in this case, but not in general (you can prove it via Bezout's identity).
– BMO
1 hour ago

is the gcd in gcd trick valid? What if a is not coprime with c?
– Jo King
1 hour ago

@jo-king If p divides a and c, it should divide c-a so b.
– david
1 hour ago

@JoKing: It is in this case, but not in general (you can prove it via Bezout's identity).
– BMO
1 hour ago

add a comment |

JavaScript (ES6), 54 bytes

Returns $0$ or $1$.

(a,b,c)=>(g=(x,y=a)=>y?g(y,x%y):x)(b)*g(c)==a<b&a+b==c

Try it online!

How?

edited 40 mins ago

answered 1 hour ago

Arnauld

72.4k689305

add a comment |

JavaScript (ES6), 54 bytes

Returns $0$ or $1$.

(a,b,c)=>(g=(x,y=a)=>y?g(y,x%y):x)(b)*g(c)==a<b&a+b==c

Try it online!

How?

edited 40 mins ago

answered 1 hour ago

Arnauld

72.4k689305

add a comment |

JavaScript (ES6), 54 bytes

Returns $0$ or $1$.

(a,b,c)=>(g=(x,y=a)=>y?g(y,x%y):x)(b)*g(c)==a<b&a+b==c

Try it online!

How?

edited 40 mins ago

answered 1 hour ago

Arnauld

72.4k689305

JavaScript (ES6), 54 bytes

Returns $0$ or $1$.

(a,b,c)=>(g=(x,y=a)=>y?g(y,x%y):x)(b)*g(c)==a<b&a+b==c

Try it online!

How?

edited 40 mins ago

answered 1 hour ago

Arnauld

72.4k689305

edited 40 mins ago

answered 1 hour ago

Arnauld

72.4k689305

answered 1 hour ago

Arnauld

72.4k689305

answered 1 hour ago

Arnauld

72.4k689305

add a comment |

Haskell, 48 38 bytes

^{-10 bytes due to TFeld's gcd trick!}

g [a,b,c]=a<b&&a+b==c&&gcd(gcd a b)c<2

Try it online!

Explanation

The first two conditions a < b and a + b == c are obvious, the third uses TFeld's intuition:

Let us write $d = gcd(a,b)$. With Bézout's identity we can write $d = U cdot a + V cdot b$ and similarly $e = gcd(d,c) = X cdot d + Y cdot c$.

edited 39 mins ago

answered 1 hour ago

BMO

11.5k22186

add a comment |

Haskell, 48 38 bytes

^{-10 bytes due to TFeld's gcd trick!}

g [a,b,c]=a<b&&a+b==c&&gcd(gcd a b)c<2

Try it online!

Explanation

The first two conditions a < b and a + b == c are obvious, the third uses TFeld's intuition:

Let us write $d = gcd(a,b)$. With Bézout's identity we can write $d = U cdot a + V cdot b$ and similarly $e = gcd(d,c) = X cdot d + Y cdot c$.

edited 39 mins ago

answered 1 hour ago

BMO

11.5k22186

add a comment |

Haskell, 48 38 bytes

^{-10 bytes due to TFeld's gcd trick!}

g [a,b,c]=a<b&&a+b==c&&gcd(gcd a b)c<2

Try it online!

Explanation

The first two conditions a < b and a + b == c are obvious, the third uses TFeld's intuition:

Let us write $d = gcd(a,b)$. With Bézout's identity we can write $d = U cdot a + V cdot b$ and similarly $e = gcd(d,c) = X cdot d + Y cdot c$.

edited 39 mins ago

answered 1 hour ago

BMO

11.5k22186

Haskell, 48 38 bytes

^{-10 bytes due to TFeld's gcd trick!}

g [a,b,c]=a<b&&a+b==c&&gcd(gcd a b)c<2

Try it online!

Explanation

The first two conditions a < b and a + b == c are obvious, the third uses TFeld's intuition:

Let us write $d = gcd(a,b)$. With Bézout's identity we can write $d = U cdot a + V cdot b$ and similarly $e = gcd(d,c) = X cdot d + Y cdot c$.

edited 39 mins ago

answered 1 hour ago

BMO

11.5k22186

edited 39 mins ago

answered 1 hour ago

BMO

11.5k22186

answered 1 hour ago

BMO

11.5k22186

answered 1 hour ago

BMO

11.5k22186

add a comment |

Jelly, 10 7 bytes

:<ƝḋgƝe

Try it online!

How it works

:<ƝḋgƝe  Main link. Argument: [a, b, c] (positive integers)



 <Ɲ      Less than neighbors; yield [(a < b), (b < c)].

:        Integer division; yield [a : (a < b), b : (b < c), c].

         The quotient is +oo if the divisor is 0.

    gƝ   GCD neighbors; yield [gcd(a, b), gcd(b, c)].

   ḋ     Dot product; yield (a : (a < b) × gcd(a, b) + b : (b < c) × gcd(b, c)).

      e  Check if the result exists in [a, b, c].

edited 5 mins ago

answered 25 mins ago

Dennis♦

186k32296735

add a comment |

Jelly, 10 7 bytes

:<ƝḋgƝe

Try it online!

How it works

:<ƝḋgƝe  Main link. Argument: [a, b, c] (positive integers)



 <Ɲ      Less than neighbors; yield [(a < b), (b < c)].

:        Integer division; yield [a : (a < b), b : (b < c), c].

         The quotient is +oo if the divisor is 0.

    gƝ   GCD neighbors; yield [gcd(a, b), gcd(b, c)].

   ḋ     Dot product; yield (a : (a < b) × gcd(a, b) + b : (b < c) × gcd(b, c)).

      e  Check if the result exists in [a, b, c].

edited 5 mins ago

answered 25 mins ago

Dennis♦

186k32296735

add a comment |

Jelly, 10 7 bytes

:<ƝḋgƝe

Try it online!

How it works

:<ƝḋgƝe  Main link. Argument: [a, b, c] (positive integers)



 <Ɲ      Less than neighbors; yield [(a < b), (b < c)].

:        Integer division; yield [a : (a < b), b : (b < c), c].

         The quotient is +oo if the divisor is 0.

    gƝ   GCD neighbors; yield [gcd(a, b), gcd(b, c)].

   ḋ     Dot product; yield (a : (a < b) × gcd(a, b) + b : (b < c) × gcd(b, c)).

      e  Check if the result exists in [a, b, c].

edited 5 mins ago

answered 25 mins ago

Dennis♦

186k32296735

Jelly, 10 7 bytes

:<ƝḋgƝe

Try it online!

How it works

:<ƝḋgƝe  Main link. Argument: [a, b, c] (positive integers)



 <Ɲ      Less than neighbors; yield [(a < b), (b < c)].

:        Integer division; yield [a : (a < b), b : (b < c), c].

         The quotient is +oo if the divisor is 0.

    gƝ   GCD neighbors; yield [gcd(a, b), gcd(b, c)].

   ḋ     Dot product; yield (a : (a < b) × gcd(a, b) + b : (b < c) × gcd(b, c)).

      e  Check if the result exists in [a, b, c].

edited 5 mins ago

answered 25 mins ago

Dennis♦

186k32296735

edited 5 mins ago

answered 25 mins ago

Dennis♦

186k32296735

answered 25 mins ago

Dennis♦

186k32296735

answered 25 mins ago

Dennis♦

186k32296735

add a comment |

Japt, 16 14 bytes

<V&Näj ×&U+V¥W

Try it

edited 56 mins ago

answered 1 hour ago

Shaggy

18.9k21666

add a comment |

Japt, 16 14 bytes

<V&Näj ×&U+V¥W

Try it

edited 56 mins ago

answered 1 hour ago

Shaggy

18.9k21666

add a comment |

Japt, 16 14 bytes

<V&Näj ×&U+V¥W

Try it

edited 56 mins ago

answered 1 hour ago

Shaggy

18.9k21666

Japt, 16 14 bytes

<V&Näj ×&U+V¥W

Try it

edited 56 mins ago

answered 1 hour ago

Shaggy

18.9k21666

edited 56 mins ago

answered 1 hour ago

Shaggy

18.9k21666

answered 1 hour ago

Shaggy

18.9k21666

answered 1 hour ago

Shaggy

18.9k21666

add a comment |

J, 27 bytes

(+/=2*{:)*({.<1{])*1=+./ .*

Try it online!

Inspired by Jo King's Perl solution

edited 31 mins ago

answered 38 mins ago

Galen Ivanov

6,34711032

add a comment |

J, 27 bytes

(+/=2*{:)*({.<1{])*1=+./ .*

Try it online!

Inspired by Jo King's Perl solution

edited 31 mins ago

answered 38 mins ago

Galen Ivanov

6,34711032

add a comment |

J, 27 bytes

(+/=2*{:)*({.<1{])*1=+./ .*

Try it online!

Inspired by Jo King's Perl solution

edited 31 mins ago

answered 38 mins ago

Galen Ivanov

6,34711032

J, 27 bytes

(+/=2*{:)*({.<1{])*1=+./ .*

Try it online!

Inspired by Jo King's Perl solution

edited 31 mins ago

answered 38 mins ago

Galen Ivanov

6,34711032

edited 31 mins ago

answered 38 mins ago

Galen Ivanov

6,34711032

answered 38 mins ago

Galen Ivanov

6,34711032

answered 38 mins ago

Galen Ivanov

6,34711032

add a comment |

If this is an answer to a challenge…

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…Be sure to follow the challenge specification. However, please refrain from exploiting obvious loopholes. Answers abusing any of the standard loopholes are considered invalid. If you think a specification is unclear or underspecified, comment on the question instead.

…Try to optimize your score. For instance, answers to code-golf challenges should attempt to be as short as possible. You can always include a readable version of the code in addition to the competitive one.
Explanations of your answer make it more interesting to read and are very much encouraged.

…Include a short header which indicates the language(s) of your code and its score, as defined by the challenge.

More generally…

…Please make sure to answer the question and provide sufficient detail.

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This page is only for reference, If you need detailed information, please check here

Find if a list is an ABC-triple

Input/Output

Test cases

Rules

Input/Output

Test cases

Rules

Input/Output

Test cases

Rules

Input/Output

Test cases

Rules

8 Answers 8

Perl 6, 33 bytes

Explanation

05AB1E, 12 11 bytes

Python 2, 69 67 63 62 bytes

Python 3, 58 bytes

JavaScript (ES6), 54 bytes

How?

Haskell, 48 38 bytes

Explanation

Jelly, 10 7 bytes

How it works

Japt, 16 14 bytes

J, 27 bytes

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8 Answers 8

8 Answers 8

Perl 6, 33 bytes

Explanation

Perl 6, 33 bytes

Explanation

Perl 6, 33 bytes

Explanation

Perl 6, 33 bytes

Explanation

05AB1E, 12 11 bytes

05AB1E, 12 11 bytes

05AB1E, 12 11 bytes

05AB1E, 12 11 bytes

Python 2, 69 67 63 62 bytes

Python 3, 58 bytes

Python 2, 69 67 63 62 bytes

Python 3, 58 bytes

Python 2, 69 67 63 62 bytes

Python 3, 58 bytes

Python 2, 69 67 63 62 bytes

Python 3, 58 bytes

JavaScript (ES6), 54 bytes

How?

JavaScript (ES6), 54 bytes

How?

JavaScript (ES6), 54 bytes

How?

JavaScript (ES6), 54 bytes

How?

Haskell, 48 38 bytes

Explanation

Haskell, 48 38 bytes

Explanation

Haskell, 48 38 bytes

Explanation

Haskell, 48 38 bytes

Explanation

Jelly, 10 7 bytes

How it works

Jelly, 10 7 bytes

How it works

Jelly, 10 7 bytes

How it works

Jelly, 10 7 bytes

How it works

Japt, 16 14 bytes

Japt, 16 14 bytes

Japt, 16 14 bytes

8 Answers
8

8 Answers
8

8 Answers
8