Von Staudt–Clausen theorem

In number theory, the von Staudt–Clausen theorem is a result determining the fractional part of Bernoulli numbers, found independently by Karl 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, then we obtain an integer; that is, B 2 n + ∑ ( p − 1 ) | 2 n 1 p ∈ Z .

Source: Wikipedia — Von Staudt–Clausen theorem (CC BY-SA 4.0)

Von Staudt–Clausen theorem

In number theory, the von Staudt–Clausen theorem is a result determining the fractional part of Bernoulli numbers, found independently by Karl 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, then we obtain an integer; that is, B 2 n + ∑ ( p − 1 ) | 2 n 1 p ∈ Z .

Source: Wikipedia "Von Staudt–Clausen theorem" · CC BY-SA 4.0

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