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?

It it is not, please tell me also!

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

Thank you a lot.

2. I don't know the answer to that question, but it looks as though it may be related to the Staudt–Clausen theorem.

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