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Proof Question (1 Viewer)

SB257426

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

Screen Shot 2023-01-23 at 12.31.18 pm.jpg

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

pikachu975

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

View attachment 37559

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
 

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