Prove that for all integers a, b, and c,
(a) if a divides b − 1 and a divides c − 1, then a divides bc − 1.
(b) if a divides b, then for all natural numbers n,
(c) if a is odd, c > 0, c divides a, and c divides a + 2, then c = 1.
(d) if there exist integers m and n such that am + bn = 1 and , then c does not divide a or c does not divide b.
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