Word Count : 168

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Assume that (5\mid (a^{2}-2b^{2})). We prove that this forces (5\mid a) and (5\mid b), which will establish the contrapositive. Working modulo (5), the quadratic residues are [ 0^{2}\equiv 0,; 1^{2}\equiv 1,; 2^{2}\equiv 4,; _____ _________ _____ _____ ___ ______ _________ __________ _______.
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