Euclid's lemma: Difference between revisions
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In [[number theory]], '''Euclid's lemma''', named after the ancient Greek geometer and number theorist [[Euclid]] of Alexandria, states that if a [[prime number]] ''p'' is a divisor of the [[multiplication|product]] ''ab'' | In [[number theory]], '''Euclid's lemma''', named after the ancient Greek geometer and number theorist [[Euclid]] of Alexandria, states that if a [[prime number]] ''p'' is a divisor of the [[multiplication|product]] ''ab'' then either ''p'' is a divisor of ''a'' or ''p'' is a divisor of ''b''. | ||
Euclid's lemma is used in the proof of the [[unique factorization theorem]], which states that a number cannot have more than one prime factorization. | Euclid's lemma is used in the proof of the [[unique factorization theorem]], which states that a number cannot have more than one prime factorization. | ||
[[category:Mathematics Workgroup]] | [[category:Mathematics Workgroup]] | ||
Revision as of 16:58, 31 July 2007
In number theory, Euclid's lemma, named after the ancient Greek geometer and number theorist Euclid of Alexandria, states that if a prime number p is a divisor of the product ab then either p is a divisor of a or p is a divisor of b.
Euclid's lemma is used in the proof of the unique factorization theorem, which states that a number cannot have more than one prime factorization.