Euclid's lemma (English, noun)
expansion: Euclid's lemma (uncountable)
Senses:
topics: mathematics
number-theory
sciences
glosses: The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;
tags: uncountable
topics: mathematics
number-theory
sciences
glosses: The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;
slightly more generally, the proposition that for integers a, b, c, if a divides bc and gcd(a, b) = 1, then a divides c;
(algebra, by generalisation) the proposition that for elements a, b, c of a given principal ideal domain, if a divides bc and gcd(a, b) = 1, then a divides c.
slightly more generally, the proposition that for integers a, b, c, if a divides bc and gcd(a, b) = 1, then a divides c;
tags: uncountable
topics: algebra
mathematics
number-theory
sciences
glosses: The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;
slightly more generally, the proposition that for integers a, b, c, if a divides bc and gcd(a, b) = 1, then a divides c;
(algebra, by generalisation) the proposition that for elements a, b, c of a given principal ideal domain, if a divides bc and gcd(a, b) = 1, then a divides c.
the proposition that for elements a, b, c of a given principal ideal domain, if a divides bc and gcd(a, b) = 1, then a divides c.
tags: uncountable
Forms:
form: Euclid's Lemma
tags: alternative