Euclid's lemma

noun3

1. •
   The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;

   • In our discussion of Euclid's lemma (Corollary 2.18), we noted that the uniqueness of factorization of integers is a fact that we often take for granted given the way it is introduced in school. — 2008
2. •
   slightly more generally, the proposition that for integers a, b, c, if a divides bc and gcd(a, b) = 1, then a divides c;
3. •
   the proposition that for elements a, b, c of a given principal ideal domain, if a divides bc and gcd(a, b) = 1, then a divides c.