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Math Help - ...sides has length divisible by 5

  1. #1
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    ...sides has length divisible by 5

    Prove that in a right triangle with integer sides, one of the three sides has length divisible by 5.
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  2. #2
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    Quote Originally Posted by NikoBellic View Post
    Prove that in a right triangle with integer sides, one of the three sides has length divisible by 5.
    Where exactly are you stuck on this?
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    if m=0 mod 5 then b=2mn = 0 mod 5



    1 and 4 are the only QR's modulo 5

    So m^2 and n^2 are either 1 or 4.

    If m^2 = n^2 mod 5 then a=m^2-n^2 = 0 mod 5

    if m^2 != n^2 mod 5 then c=m^2+n^2 = 1+4=0 mod 5
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