I am really confused for the following proof question and am unsure where to start (I don't really get the hint)

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I would really appreciate it if anyone helped me out with this question

Contrapositive - if p is prime, then if p|ab then p|a or p|b (Euclid's lemma)

a = p1, b = p/p1

The contrapositive states that p is prime, and p1 is a prime divisor of p. That means that p1 must equal 1 or p.

Case 1: p1 = 1, a = 1, b = p

p|ab = p|p

p|a = p|1

p|p is true

So that means the contrapositive holds true in this case

Case 2: p1 = p, a = p, b = 1

p|ab = p|p

p|a = p|p

Holds true here as well

So then the contrapositive is true.

Probably didn't set it out that well but yea that's how I'd go about it