--- In

primenumbers@yahoogroups.com, "S. R. Sudarshan Iyengar"

<sudarshanmysore@...> wrote:

>

> Here goes a nice problem... IT would be nice if someone can give me

> links/references where I can find more details about this problem.

>

> Given a prime P its easy to see that it always divides 1+ 2 + .. +

(p-1)

>

> But it in fact divides 1^k + 2^k + ... + (p-1)^k for all k except 0

> and p-1.

>

> Its obvious if k is odd. But is there any way of proving it when k

is

> even?

>

> Regards,

> Sudarshan

>

This is not a property of the prime numbers but of the natural

numbers: put n instead of p, or, if you want, 2n-1 (odd numbers).

WDS