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- Euclids_lemma abstract "In number theory, Euclid's lemma 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. It is also called Euclid's first theorem although that name more properly belongs to the side-angle-side condition for showing that triangles are congruent. For example, 133 × 143 = 19019, and since 19019 is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well. In fact, 133 = 19 × 7.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.".
- Euclids_lemma wikiPageID "826617".
- Euclids_lemma wikiPageLength "6977".
- Euclids_lemma wikiPageOutDegree "25".
- Euclids_lemma wikiPageRevisionID "679951830".
- Euclids_lemma wikiPageWikiLink Bxc3xa9zouts_identity.
- Euclids_lemma wikiPageWikiLink Carl_Friedrich_Gauss.
- Euclids_lemma wikiPageWikiLink Category:Articles_containing_proofs.
- Euclids_lemma wikiPageWikiLink Category:Lemmas.
- Euclids_lemma wikiPageWikiLink Category:Theorems_about_prime_numbers.
- Euclids_lemma wikiPageWikiLink Commutative_ring.
- Euclids_lemma wikiPageWikiLink Composite_number.
- Euclids_lemma wikiPageWikiLink Congruence_(geometry).
- Euclids_lemma wikiPageWikiLink Coprime_integers.
- Euclids_lemma wikiPageWikiLink Disquisitiones_Arithmeticae.
- Euclids_lemma wikiPageWikiLink Euclid.
- Euclids_lemma wikiPageWikiLink Euclidean_algorithm.
- Euclids_lemma wikiPageWikiLink Euclids_Elements.
- Euclids_lemma wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Euclids_lemma wikiPageWikiLink Gausss_lemma_(number_theory).
- Euclids_lemma wikiPageWikiLink Jean_Prestet.
- Euclids_lemma wikiPageWikiLink Lemma_(mathematics).
- Euclids_lemma wikiPageWikiLink Logical_equivalence.
- Euclids_lemma wikiPageWikiLink Number_theory.
- Euclids_lemma wikiPageWikiLink Prime_element.
- Euclids_lemma wikiPageWikiLink Prime_number.
- Euclids_lemma wikiPageWikiLink Solution_of_triangles.
- Euclids_lemma wikiPageWikiLink Triangle.
- Euclids_lemma wikiPageWikiLinkText "Euclid's first theorem".
- Euclids_lemma wikiPageWikiLinkText "Euclid's lemma".
- Euclids_lemma hasPhotoCollection Euclids_lemma.
- Euclids_lemma wikiPageUsesTemplate Template:Distinguish.
- Euclids_lemma wikiPageUsesTemplate Template:Math.
- Euclids_lemma wikiPageUsesTemplate Template:Nowrap_begin.
- Euclids_lemma wikiPageUsesTemplate Template:Nowrap_end.
- Euclids_lemma wikiPageUsesTemplate Template:Reflist.
- Euclids_lemma wikiPageUsesTemplate Template:Rp.
- Euclids_lemma subject Category:Articles_containing_proofs.
- Euclids_lemma subject Category:Lemmas.
- Euclids_lemma subject Category:Theorems_about_prime_numbers.
- Euclids_lemma hypernym Lemma.
- Euclids_lemma type Thing.
- Euclids_lemma comment "In number theory, Euclid's lemma 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. It is also called Euclid's first theorem although that name more properly belongs to the side-angle-side condition for showing that triangles are congruent. For example, 133 × 143 = 19019, and since 19019 is divisible by 19, the lemma implies that one or both of 133 or 143 must be as well.".
- Euclids_lemma label "Euclid's lemma".
- Euclids_lemma differentFrom Euclidean_algorithm.
- Euclids_lemma differentFrom Euclids_theorem.
- Euclids_lemma sameAs موضوعة_أقليدس.
- Euclids_lemma sameAs Lema_dEuclides.
- Euclids_lemma sameAs Eukleidovo_lemma.
- Euclids_lemma sameAs Lemma_von_Euklid.
- Euclids_lemma sameAs Lema_de_Euclides.
- Euclids_lemma sameAs لم_اقلیدس.
- Euclids_lemma sameAs Lemme_dEuclide.
- Euclids_lemma sameAs הלמה_של_אוקלידס.
- Euclids_lemma sameAs Lemma_di_Euclide.
- Euclids_lemma sameAs ユークリッドの補題.
- Euclids_lemma sameAs Евклид_леммасы.
- Euclids_lemma sameAs 유클리드의_보조_정리.
- Euclids_lemma sameAs Lemma_vum_Euklid.
- Euclids_lemma sameAs Lemat_Euklidesa.
- Euclids_lemma sameAs m.03f88j.
- Euclids_lemma sameAs Лемма_Евклида.
- Euclids_lemma sameAs Euclids_lemma.
- Euclids_lemma sameAs Evklidova_lema.
- Euclids_lemma sameAs Лема_Евкліда.
- Euclids_lemma sameAs Q206793.
- Euclids_lemma sameAs Q206793.
- Euclids_lemma sameAs 欧几里得引理.
- Euclids_lemma wasDerivedFrom Euclids_lemmaoldid=679951830.
- Euclids_lemma isPrimaryTopicOf Euclids_lemma.