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Euclid's lemma (Theorem)

If $a$ , $b$ , and $c$ are integers (or, more generally, elements of a principal ideal domain) with $a | bc$ and $\mbox{gcd}(a,b)=1$ , then $a | c$ .




"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

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 5726 times total.

Classification:
AMS MSC11A05 (Number theory :: Elementary number theory :: Multiplicative structure; Euclidean algorithm; greatest common divisors)

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