PlanetMath: Euclid's lemma

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Euclid's lemma

(Theorem)

If , , and are integers (or, more generally, elements of a principal ideal domain) with $a \vert bc$ and gcd, then $a \vert c$ .

"Euclid's lemma" is owned by KimJ.

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Keywords:

number theory

Attachments:: Euclid's lemma proof (Proof) by akrowne
alternative proof of Euclid's lemma (Proof) by alozano

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Cross-references: principal ideal domain, integers
There are 2 references to this entry.

This is version 4 of Euclid's lemma, born on 2001-10-16, modified 2004-12-29.
Object id is 249, canonical name is EuclidsLemma.
Accessed 4755 times total.

Classification:

11A05 (Number theory :: Elementary number theory :: Multiplicative structure; Euclidean algorithm; greatest common divisors)

Pending Errata and Addenda

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