Euclid's Lemma/Proof 1

Theorem

Let $a, b, c \in \Z$.

Let $a \divides b c$, where $\divides$ denotes divisibility.

Let $a \perp b$, where $\perp$ denotes relative primeness.

Then $a \divides c$.

Proof

Follows directly from Integers are Euclidean Domain.

$\blacksquare$

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Source of Name

This entry was named for Euclid.

Also see

• Euclid's Lemma for Prime Divisors