Prove that in a right triangle with integer sides, one of the three sides has length divisible by 5.
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Originally Posted by NikoBellic 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?
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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