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Von Staudt-Clausen theorem
In number theory, the von Staudt-Clausen theorem is a result on the fractional part of Bernoulli numbers. Specifically, if we add 1/p to Bn for every prime p such that p − 1 divides n, we obtain an integer.
This fact immediately allows us to characterize the denominators of the non-zero Bernoulli numbers Bn as the product of all primes p such that p − 1 divides n; consequently the denominators are square-free and divisible by 6.
The result is named for Karl von Staudt (1798-1867) and Thomas Clausen (1801-1885), who independently discovered the result in 1840.
11-30-2008 18:11:33
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details