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 Let a and b be integers and m be a positive integer

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 Let a and b be integers and m be a positive integer. Prove that the linear congruence equation ax ≡ b mod m has an integer solution x if and only if gcd(a, m) divides b. Note: A linear congruence equation ax ≡ b mod m has an integer solution x means there is an integer x such that ax ≡ b mod m.