Prove or disprove the following statements: (a) Let a and n be integers, if a|n, then a|n^2 (b) Let a and n be integers if a|n^2, then a|n. (c) Let a, n, m be integers, if a|n and a|m, then a|(n · m). (d) Let a, n, m be integers, if a|(n · m), then a|n or a|m. (e) Let a, n, m be integers, if a|(n · m), then a|n a
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Prove or disprove the following statements:
(a) Let a and n be integers, if a|n, then a|n^2
(b) Let a and n be integers if a|n^2, then a|n.
(c) Let a, n, m be integers, if a|n and a|m, then a|(n · m).
(d) Let a, n, m be integers, if a|(n · m), then a|n or a|m.
(e) Let a, n, m be integers, if a|(n · m), then a|n and a|m
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