Matches in DBpedia 2014 for { ?s ?p 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). }
Showing items 1 to 1 of
1
with 100 items per page.
- 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)".