(a) Let m, n be coprime integers, and suppose a is an integer which is divisible by both m and n. Prove that mn divides a. (b) Show that the conclusion of part (a) is false if m and n are not coprime (i.e., show that if m and n are not coprime, there exists an integer a such that mla and n/a, but mn does not divide a). (c) Show that if hef(x, m) = 1 and hcf(y,m): = = 1, then hcf(xy, m) = 1.

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