# Euclid's lemma

Let $$a$$ and $$b$$ be any integers. If $$p$$ is prime and if $$p$$ divides $$ab$$, then either $$p$$ divides $$a$$ or $$p$$ divides $$b$$.
Let $$a_1, a_2, \ldots, a_n$$ be integers. If $$p$$ is a prime number and if $$p \mid a_1a_2{\ldots}a_n$$, then $$p \mid a_i$$ for some $$i$$ with $$1 \le i \le n$$.