Let p be a prime and n a positive integer. If pa|n, but , we say that pa exactly divides n...

Let p be a prime and n a positive integer. If pa|n, but , we say that pa exactly divides n, and we write pa ǁ n.

a) Show that if pa ǁ m and pb ǁ n, then pa+b ǁ mn.

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b) Show that if pa ǁ m, then pka ǁ mk.

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c) Show that if pa ǁ m and pb ǁ n with a ≠ b, then pmin (a,b) ǁ (m + n).