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- Euclid's_lemma abstract "In number theory, Euclid's lemma (also called Euclid's first theorem) is a lemma that captures a fundamental property of prime numbers, namely: If a prime divides the product of two numbers, it must divide at least one of those numbers. For example since 133 × 143 = 19019 is divisible by 19, one or both of 133 or 143 must be as well. In fact, 19 × 7 = 133.This property is the key in the proof of the fundamental theorem of arithmetic. It is used to define prime elements, a generalization of prime numbers to arbitrary commutative rings.The lemma is not true for composite numbers. For example, 4 does not divide 6 and 4 does not divide 10, yet 4 does divide their product, 60.".
- Euclid's_lemma wikiPageID "826617".
- Euclid's_lemma wikiPageRevisionID "604392742".
- Euclid's_lemma hasPhotoCollection Euclid's_lemma.
- Euclid's_lemma subject Category:Articles_containing_proofs.
- Euclid's_lemma subject Category:Lemmas.
- Euclid's_lemma subject Category:Theorems_about_prime_numbers.
- Euclid's_lemma type Abstraction100002137.
- Euclid's_lemma type Communication100033020.
- Euclid's_lemma type Lemma106751833.
- Euclid's_lemma type Lemmas.
- Euclid's_lemma type Message106598915.
- Euclid's_lemma type Proposition106750804.
- Euclid's_lemma type Statement106722453.
- Euclid's_lemma type Theorem106752293.
- Euclid's_lemma type TheoremsAboutPrimeNumbers.
- Euclid's_lemma comment "In number theory, Euclid's lemma (also called Euclid's first theorem) is a lemma that captures a fundamental property of prime numbers, namely: If a prime divides the product of two numbers, it must divide at least one of those numbers. For example since 133 × 143 = 19019 is divisible by 19, one or both of 133 or 143 must be as well. In fact, 19 × 7 = 133.This property is the key in the proof of the fundamental theorem of arithmetic.".
- Euclid's_lemma label "Euclid's lemma".
- Euclid's_lemma label "Lema de Euclides".
- Euclid's_lemma label "Lemat Euklidesa".
- Euclid's_lemma label "Lemma di Euclide".
- Euclid's_lemma label "Lemma von Euklid".
- Euclid's_lemma label "Lemme d'Euclide".
- Euclid's_lemma label "Лемма Евклида".
- Euclid's_lemma label "موضوعة أقليدس".
- Euclid's_lemma label "欧几里得引理".
- Euclid's_lemma sameAs Eukleidovo_lemma.
- Euclid's_lemma sameAs Lemma_von_Euklid.
- Euclid's_lemma sameAs Lema_de_Euclides.
- Euclid's_lemma sameAs Lemme_d'Euclide.
- Euclid's_lemma sameAs Lemma_di_Euclide.
- Euclid's_lemma sameAs Lemat_Euklidesa.
- Euclid's_lemma sameAs m.03f88j.
- Euclid's_lemma sameAs Q206793.
- Euclid's_lemma sameAs Q206793.
- Euclid's_lemma sameAs Euclid's_lemma.
- Euclid's_lemma wasDerivedFrom Euclid's_lemma?oldid=604392742.
- Euclid's_lemma isPrimaryTopicOf Euclid's_lemma.