Why does p|4q also mean p|q if p is odd?

Question

It might be a simple question but it's in the answers and I want to know.

score 5 · Answer 1 · answered Nov 19 '13 at 23:05

5

Because $p$ and $4$ would be relatively prime. This is a general statement. If $p|ab$ and $(p,a)=1$, then $p|b$.

answered Nov 19 '13 at 23:05

LASV

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score 2 · Answer 2 · answered Nov 19 '13 at 23:08

2

For this, we should cite Euclid's Lemma: if $p|ab$, then $p|a$ or $p|ab$, or both. If $p$ is odd, then $p$ does not divide $4$. So $p$ must divide $b$.

answered Nov 19 '13 at 23:08

Newb

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Why does p|4q also mean p|q if p is odd?

2 Answers2