Let p be a prime integer. Prove that is [a][b] = [0] onZ p then either [a] = [0]

Question

Let p be a prime integer. Prove that is [a][b] = [0] onZp then either [a] = [0] or [b]=[0]. I wouldn't think that this would be hard to prove but I can'tseem to figure it out. I hope you all understand the notation. Itsall talking about congruence classes under multiplication. Let p be a prime integer. Prove that is [a][b] = [0] onZp then either [a] = [0] or [b]=[0]. I wouldn't think that this would be hard to prove but I can'tseem to figure it out. I hope you all understand the notation. Itsall talking about congruence classes under multiplication.

Explanation / Answer

Think about it this way... What does it mean for a number to beprime? Then look at yuor equation, clearly if [a][b] is congruentto [0] in mod p then ab|p, but we said p was prime so this isimpossible, thus either a or b have to be zero :)

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