Let x and y be even integers. Prove that x 2 y2 (mod 16) if and only if either (1) x 0

Chapter 4, Problem 4.24

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Let x and y be even integers. Prove that x 2 y2 (mod 16) if and only if either (1) x 0 (mod 4) andy 0 (mod 4) or (2) x 2 (mod 4) and y 2 (mod 4).

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