Solution
= Solution
Every integer $n>1$ is a product of primes, uniquely up to order. Existence follows by <strong induction>: if $n$ is not prime, factor it into smaller positive integers and apply induction. For uniqueness, if
$$
p_1\cdots p_r=q_1\cdots q_s,
$$
Euclid's lemma makes $p_1$ divide some $q_j$, hence equal it. Cancel that prime and induct on the number of factors.