Euclid's lemma

短语

释义与例句

n.
  1. 1.

    The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;

    不可数 数学
  2. 2.

    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;

    不可数 数学
  3. 3.

    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.

    不可数 数学

词源

Named after ancient Greek mathematician Euclid of Alexandria (fl. 300 BCE). A version of the proposition appears in Book VII of his Elements.

来源：wiktionary