Euclid's lemma
nounEtymology
Named after ancient Greek mathematician Euclid of Alexandria (fl. 300 BCE). A version of the proposition appears in Book VII of his Elements.
Definitions
The proposition that if a prime number p divides an arbitrary product ab of integers,…
The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;
- If a and b are not relatively prime, then the conclusion of Euclid's lemma may fail to hold. A specific example: 12#92;mid 9#92;cdot 8, but 12#92;nmid 9 and 12#92;nmid 8.
- In our discussion of Euclid's lemma (Corollary 2.18), we noted that the uniqueness of factorization of integers is a fact that we often take for granted given the way it is introduced in school.
The neighborhood
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sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA