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- Wolstenholme's_theorem abstract "In mathematics, Wolstenholme's theorem states that for a prime number p > 3, the congruenceholds, where the parentheses denote a binomial coefficient. For example, with p = 7, this says that 1716 is one more than a multiple of 343. An equivalent formulation is the congruenceThe theorem was first proved by Joseph Wolstenholme in 1862. In 1819, Charles Babbage showed the same congruence modulo p2, which holds for all primes p (for p=2 only in the second formulation). The second formulation of Wolstenholme's theorem is due to J. W. L. Glaisher and is inspired by Lucas' theorem.No known composite numbers satisfy Wolstenholme's theorem and it is conjectured that there are none (see below). A prime that satisfies the congruence modulo p4 is called a Wolstenholme prime (see below).As Wolstenholme himself established, his theorem can also be expressed as a pair of congruences for (generalized) harmonic numbers:(Congruences with fractions make sense, provided that the denominators are coprime to the modulus.)For example, with p=7, the first of these says that the numerator of 49/20 is a multiple of 49, while the second says the numerator of 5369/3600 is a multiple of 7.".
- Wolstenholme's_theorem wikiPageExternalLink 1111.3057.
- Wolstenholme's_theorem wikiPageExternalLink books?id=KrA-AAAAYAAJ&pg=PA46.
- Wolstenholme's_theorem wikiPageExternalLink books?id=vL0KAAAAIAAJ&pg=PA35.
- Wolstenholme's_theorem wikiPageExternalLink aa7144.pdf.
- Wolstenholme's_theorem wikiPageExternalLink page.php?sort=Wolstenholme.
- Wolstenholme's_theorem wikiPageExternalLink Wieferich.status.
- Wolstenholme's_theorem wikiPageID "1113185".
- Wolstenholme's_theorem wikiPageRevisionID "579586973".
- Wolstenholme's_theorem hasPhotoCollection Wolstenholme's_theorem.
- Wolstenholme's_theorem subject Category:Articles_containing_proofs.
- Wolstenholme's_theorem subject Category:Classes_of_prime_numbers.
- Wolstenholme's_theorem subject Category:Factorial_and_binomial_topics.
- Wolstenholme's_theorem subject Category:Theorems_about_prime_numbers.
- Wolstenholme's_theorem type Abstraction100002137.
- Wolstenholme's_theorem type Class107997703.
- Wolstenholme's_theorem type ClassesOfPrimeNumbers.
- Wolstenholme's_theorem type Collection107951464.
- Wolstenholme's_theorem type Communication100033020.
- Wolstenholme's_theorem type Group100031264.
- Wolstenholme's_theorem type Message106598915.
- Wolstenholme's_theorem type Proposition106750804.
- Wolstenholme's_theorem type Statement106722453.
- Wolstenholme's_theorem type Theorem106752293.
- Wolstenholme's_theorem type TheoremsAboutPrimeNumbers.
- Wolstenholme's_theorem comment "In mathematics, Wolstenholme's theorem states that for a prime number p > 3, the congruenceholds, where the parentheses denote a binomial coefficient. For example, with p = 7, this says that 1716 is one more than a multiple of 343. An equivalent formulation is the congruenceThe theorem was first proved by Joseph Wolstenholme in 1862. In 1819, Charles Babbage showed the same congruence modulo p2, which holds for all primes p (for p=2 only in the second formulation).".
- Wolstenholme's_theorem label "Satz von Wolstenholme".
- Wolstenholme's_theorem label "Stelling van Wolstenholme".
- Wolstenholme's_theorem label "Teorema de Wolstenholme".
- Wolstenholme's_theorem label "Théorème de Wolstenholme".
- Wolstenholme's_theorem label "Wolstenholme's theorem".
- Wolstenholme's_theorem label "Теорема Вольстенхольма".
- Wolstenholme's_theorem label "沃尔斯滕霍尔姆定理".
- Wolstenholme's_theorem sameAs Satz_von_Wolstenholme.
- Wolstenholme's_theorem sameAs Teorema_de_Wolstenholme.
- Wolstenholme's_theorem sameAs Théorème_de_Wolstenholme.
- Wolstenholme's_theorem sameAs Stelling_van_Wolstenholme.
- Wolstenholme's_theorem sameAs m.0473p6.
- Wolstenholme's_theorem sameAs Q1724049.
- Wolstenholme's_theorem sameAs Q1724049.
- Wolstenholme's_theorem sameAs Wolstenholme's_theorem.
- Wolstenholme's_theorem wasDerivedFrom Wolstenholme's_theorem?oldid=579586973.
- Wolstenholme's_theorem isPrimaryTopicOf Wolstenholme's_theorem.