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  3. prove parts 1 2 4 5 and 6 theorem 21...

Question: prove parts 1 2 4 5 and 6 theorem 21...

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Prove parts (1), (2), (4), (5), and (6) Theorem 2.1 Let a, b, c, d denote integers. Then: (I) a b (mod m), ba (mod m), and a -b0 (mod m) are equivalent statements (2) If a-b (mod m) and b-c (mod m), then a c (mod m). (3) If a b (mod m) and c d (mod m), then a + c b + d (mod m). (4) Ifa b (mod m) and cd (mod m), then acbd (mod m). (5) If a b (mod m) and dlm, d > 0, then ab (mod d). (6) Ifa b (mod m) then ac - bc (mod mc) for c > 0.

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