Question: Define [a] = {m E Z | a: E a (mod 11)} . Let p be a prime number. Recall that J'p denotes the set

Define [a] = {m E Z | a: E a (mod 11)} . Let p be a prime number. Recall that J'p denotes the set of equivalence classes modulo 1) . Prove that a natural number n is prime if and only if the following statement is true in J\" : [a][b] = 0 implies that [a] = [O] or [b] = [0]

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