Theorem of von Staudt-Clausen

In Theory of the numbers, the theorem of von Staudt-Clausen is a result on the fractional left the numbers of Bernoulli. Precisely, if we add $\backslash \; frac\; \{1\}\; \{p\}\; \backslash ,$ with $B\_n\; \backslash ,$ for each Prime number p such as $p\; -\; 1\; \backslash ,$ divides N , we obtain a Integer.

This fact immediately allow us to characterize the denominators of the numbers of Bernoulli different from zero $B\_n\; \backslash ,$ like the product of all the prime numbers p such as $p\; -\; 1\; \backslash ,$ divides N ; consequently, the denominators are Without square and divisible by 6.

The result was named thus in the honor of Karl von Staudt (1798-1867) and Thomas Clausen (1801-1885), which independently discovered this one in 1840.

Random links:

Quins | Clube de Regatas Brasil | Misawa | HC Martigny | Yvon Lambert (hockey) | Sanborn,_le_Wisconsin

© 2007-2008 speedlook.com; article text available under the terms of GFDL, from fr.wikipedia.org