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1. Write a proof for all non-zero integers x and y, if there exist integers n...

1. Write a proof for all non-zero integers x and y, if there exist integers n and m such that xn + ym = 1, then gcd(x, y) = 1.

2. Write a proof for all non-zero integers x and y, gcd(x, y) = 1 if and only if gcd(x, y2) = 1.

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