Discussion: This is a straightforward example of a parity problem combined with proof by contradiction and unique factorization. To show the product is even one must show that at least one of a,b or c is even. This student assumes to the contrary and gets a contradiction: if a and b are both odd then so are a^2 and b^2. But then c^2 = a^2 + b^2 is the sum of two odd numbers and therefore is even, contrary to assumption.

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