For a positive integar m, let
Zm = {0, 1, ..., m-1}.
Define: +: Zm x Zm -> Zm
mul: Zm x Zm -> Zm
by taking answers modulo m (e.g., Z6 = {0,1,2,3,4,5} and (3)(5) = 15 modulo 6 = 3). Show that Zm has no divisors of zero <=> m is a prime.
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