Pythagorean triples: Difference between revisions
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A [[wp:Pythagorean_triple|Pythagorean triple]] is defined as three positive integers <math>(a, b, c)</math> where <math>a\leq b\leq c</math>, and <math>a^2+b^2=c^2.</math> They are called primitive triples if <math>a, b, c</math> are coprime. Each triple form the length of the sides of a right triangle, whose perimeter is <math>P=a+b+c</math>. |
A [[wp:Pythagorean_triple|Pythagorean triple]] is defined as three positive integers <math>(a, b, c)</math> where <math>a\leq b\leq c</math>, and <math>a^2+b^2=c^2.</math> They are called primitive triples if <math>a, b, c</math> are coprime, that is, if their pairwise greatest common denominators <math>{\rm gcd}(a, b) = {\rm gcd}(a, c) = {\rm gcd}(b, c) = 1</math>. Each triple form the length of the sides of a right triangle, whose perimeter is <math>P=a+b+c</math>. |
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==Task== |
==Task== |
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Revision as of 15:52, 28 June 2011
Pythagorean triples is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
A Pythagorean triple is defined as three positive integers where , and They are called primitive triples if are coprime, that is, if their pairwise greatest common denominators . Each triple form the length of the sides of a right triangle, whose perimeter is .
Task
How many Pythagorean triples are there with a perimeter no larger than 100? Of these, how many are primitive?
Extra: Can your program handle a max perimeter of 1,000,000? What about 10,000,000? 100,000,000?