So I am supposed to be proving that if $p_1$ and $p_2$ are distinct primes and $p_1\mid a$ and $p_2\mid a$ then $p_1p_2\mid a$, and I need to use Euclid's Lemma except as far as I understand Euclid's lemma is the converse of this statement and I have tried for the last few hours to work with Euclid's and GCDs to figure this one out and I just don't know where to start since I can't wrap my head around this one. Can anyone help me out?
Prove that if $p_1\mid a$ and $p_2\mid a$ then $p_1p_2\mid a$
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elementary-number-theory