Let (p) be a prime number and (k) a positive integer. (a) Show that if (x) is
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Let \(p\) be a prime number and \(k\) a positive integer.
(a) Show that if \(x\) is an integer such that \(x^{2} \equiv x \bmod p\), then \(x \equiv 0\) or \(1 \bmod p\).
(b) Show that if \(x\) is an integer such that \(x^{2} \equiv x \bmod p^{k}\), then \(x \equiv 0\) or \(1 \bmod p^{k}\).
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