# About Bernoulli Numbers

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• Jul 22nd 2009, 03:07 AM
gdmath
About Bernoulli Numbers
Hi everyone
While i am working on some computer algorithms, I encounter the following

$N^{(s+1)}-N=0 mod{ }Denominator[B_s]$

Where Bs is the s bernoulli number and N any integer.
Is this well known?

If it is, please provide me some internet links
It it is not, please tell me also!

(ps: I have found some equlavets of this relation)

Thank you a lot.
• Jul 22nd 2009, 06:30 AM
Opalg
I don't know the answer to that question, but it looks as though it may be related to the Staudt–Clausen theorem.
• Jul 22nd 2009, 07:20 AM
gdmath
Thank you for your reply
Yes it might be similar with Staudt–Clausen therem and it might be similar to kummer congruensies (as far i searched)

Anyway i have prepared a paper all these days (adout this)
wich unfortunatelly i do not have all the proofs (look attacment)

I want to send to some of my friends that they are in university (unfortunatelly now its summer and i have to wait until sempeber) to examine it.
However any suggestions would be very greatfull