Euclid's Lemma for Prime Divisors/Proof 1
Let $p$ be a prime number.
Let $a$ and $b$ be integers such that:
- $p \divides a b$
where $\divides$ means is a divisor of.
Then $p \divides a$ or $p \divides b$.
We have that the integers form a Euclidean domain.
The result then follows directly from Euclid's Lemma for Irreducible Elements.
Source of Name
This entry was named for Euclid.