Talk:Euclid's lemma

$a{\frac {b}{p}}=n\ ,$

and since gcd(a, p) = 1 and n is an integer, b/p must also be an integer

I'm afraid you've lost me. How can you draw this conclusion without assuming either Euclid's lemma or uniqueness of prime factorization (the first of which certainly involves circular reasoning and is thus a logical fallacy, and the secdon of which is vulnerable to the same danger since Euclid's lemma is often used for proving uniqueness of factoriazation)? Michael Hardy 20:35, 3 August 2007 (CDT)