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- Von_Staudt–Clausen_theorem abstract "In number theory, the von Staudt–Clausen theorem is a result determining the fractional part of Bernoulli numbers, found independently byKarl von Staudt (1840) and Thomas Clausen (1840).Specifically, if n is a positive integer and we add 1/p to the Bernoulli number B2n for every prime p such that p − 1 divides 2n, we obtain an integer, i.e., This fact immediately allows us to characterize the denominators of the non-zero Bernoulli numbers B2n as the product of all primes p such that p − 1 divides 2n; consequently the denominators are square-free and divisible by 6.These denominators are 6, 30, 42, 30, 66, 2730, 6, 510, 798, 330, 138, 2730, 6, 870, 14322, 510, 6, 1919190, 6, 13530, ... (sequence A002445 in OEIS)".
- Von_Staudt–Clausen_theorem wikiPageID "1084655".
- Von_Staudt–Clausen_theorem wikiPageRevisionID "598154970".
- Von_Staudt–Clausen_theorem authorlink "Karl von Staudt".
- Von_Staudt–Clausen_theorem authorlink "Thomas Clausen".
- Von_Staudt–Clausen_theorem first "Karl".
- Von_Staudt–Clausen_theorem first "Thomas".
- Von_Staudt–Clausen_theorem last "Clausen".
- Von_Staudt–Clausen_theorem last "von Staudt".
- Von_Staudt–Clausen_theorem title "von Staudt-Clausen Theorem".
- Von_Staudt–Clausen_theorem urlname "vonStaudt-ClausenTheorem".
- Von_Staudt–Clausen_theorem year "1840".
- Von_Staudt–Clausen_theorem subject Category:Theorems_in_number_theory.
- Von_Staudt–Clausen_theorem comment "In number theory, the von Staudt–Clausen theorem is a result determining the fractional part of Bernoulli numbers, found independently byKarl von Staudt (1840) and Thomas Clausen (1840).Specifically, if n is a positive integer and we add 1/p to the Bernoulli number B2n for every prime p such that p − 1 divides 2n, we obtain an integer, i.e., This fact immediately allows us to characterize the denominators of the non-zero Bernoulli numbers B2n as the product of all primes p such that p − 1 divides 2n; consequently the denominators are square-free and divisible by 6.These denominators are 6, 30, 42, 30, 66, 2730, 6, 510, 798, 330, 138, 2730, 6, 870, 14322, 510, 6, 1919190, 6, 13530, ... ".
- Von_Staudt–Clausen_theorem label "Théorème de von Staudt-Clausen".
- Von_Staudt–Clausen_theorem label "Von Staudt–Clausen theorem".
- Von_Staudt–Clausen_theorem sameAs Von_Staudt%E2%80%93Clausen_theorem.
- Von_Staudt–Clausen_theorem sameAs Théorème_de_von_Staudt-Clausen.
- Von_Staudt–Clausen_theorem sameAs Q3527230.
- Von_Staudt–Clausen_theorem sameAs Q3527230.
- Von_Staudt–Clausen_theorem wasDerivedFrom Von_Staudt–Clausen_theorem?oldid=598154970.