Phrase guide
Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.
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noun
The proposition that if a prime number p divides an arbitrary product ab of integers, then p divides a or b or both;
Definition source: English Wiktionary via Wiktextract
Usage: uncountable
Topics: mathematics, number-theory, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
noun
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;
Definition source: English Wiktionary via Wiktextract
Usage: uncountable
Topics: mathematics, number-theory, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
noun
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.
Definition source: English Wiktionary via Wiktextract
Usage: uncountable
Topics: algebra, mathematics, number-theory, sciences
No example sentence was provided for this meaning.
Synonyms: none provided
Antonyms: none provided
History
Named after ancient Greek mathematician Euclid of Alexandria (fl. 300 BCE). A version of the proposition appears in Book VII of his Elements.
