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Math Help - Pythagorean triples? 3-4-5, and 5-12-13

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    Pythagorean triples? 3-4-5, and 5-12-13

    can anyone explain this concept to me?
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    Senior Member jakncoke's Avatar
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    Re: Pythagorean triples? 3-4-5, and 5-12-13

    Basically, a pythogorean triple is just 3 positive integers which satisfy the pythogorean theorem  a^2 + b^2 = c^2 .
    So  3^2 + 4^2 = 5^2 \text{ and } 5^2 + 12^2 = 13^2
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    MHF Contributor MarkFL's Avatar
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    Re: Pythagorean triples? 3-4-5, and 5-12-13

    In a nutshell, a Pythagorean triple (a,b,c) has the property that a^2+b^2=c^2

    Perhaps the best know method for generating such triples (attributed to Euclid) is to let:

    a=m^2-n^2

    b=2mn

    c=m^2+n^2

    where n<m and m,n\in\mathbb{N}.

    A triple is said to be primitive if a,b,c are co-prime, and requires m,n to be co-prime and m-n is odd.

    Pythagorean triple - Wikipedia, the free encyclopedia
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