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Math Help - Prove if it a Pythagorean triple

  1. #1
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    Question Prove if it a Pythagorean triple

    the information given to me is :

    a triple (a, b,c ) of natural numbers is called a Pythagorean triple iFF
    a^2 + b^2 = c^2. A Pythagorean triple (a ,b ,c ) is called primitive IFF a, b, and c have no common factor.
    In the following, let u,v be elements of N such that u.v and gcd(u,v) =1, and define a= u^2 -v^2 = 2uv and c= u^2 +v^2

    I am asked 1: Is ( a,b ,c ) a Pythagorean triple
    2. If both u and v are odd, then (a,b,c)is not primitive
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  2. #2
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    The answer to question 1 is proved in your other thread. For 2, ask yourself for each of a,b,c, is it even or odd?
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  3. #3
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    Quote Originally Posted by Media_Man View Post
    The answer to question 1 is proved in your other thread. For 2, ask yourself for each of a,b,c, is it even or odd?

    thank you ! Just the hint i needed, the rest is crystal clear.

    thanks again !!
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