SOLUTION: let (a,b,c) be a primitive pythagorous triplet(a<b<c).show that c is odd.

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Question 475377: let (a,b,c) be a primitive pythagorous triplet(a
Answer by richard1234(7193) About Me  (Show Source):
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By the Pythagorean theorem,



Assume c is even. Then c^2 ≡ 0 (mod 4), and a^2 or b^2 can only be congruent to 0 or 1 mod 4, so this creates a contradiction (unless a,b,c are all divisible by 2, which still doesn't work since the triple is primitive). Hence, c must be odd.