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For a positive integar m, let Zm = {0, 1, ..., m-1}. Define: +: Zm x...

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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