Euclid's Lemma

For any two integers a and b, suppose d|ab. Then if d is relatively prime to a, then d divides b. This results appeared in Euclid's Elements, Book VII, Proposition 30.

This result is incorrectly termed "Gauss's lemma," which is an entirely different result, by Séroul (2000, pp. 10-11).

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Séroul, R. "Gauss's Lemma." §2.4.2 in Programming for Mathematicians. Berlin: Springer-Verlag, pp. 10-11, 2000.

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Euclid's Lemma

Cite this as:

Weisstein, Eric W. "Euclid's Lemma." From MathWorld--A Wolfram Web Resource.

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