Euclid's lemma

Euclid's lemma is a fundamental statement in number theory that relates to the properties of prime numbers and divisibility. It states: **If a prime number \( p \) divides the product of two integers \( a \) and \( b \) (i.e., \( p \mid (a \cdot b) \)), then \( p \) must divide at least one of those integers \( a \) or \( b \) (i.e.