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12. Bézout's identity: Let a, b = Z with gcd(a, b) = 1. Then there exists x, y = Z such that ax + by = 1. (For example, letting a = 5 and b = 7 we can use x = 10 and y=-7). Using Bézout's identity, show that for a € Z and p prime, if a ‡ 0 (mod p) then ak = 1 (mod p) for some k € Z.