Re: A nice problem...
- --- In firstname.lastname@example.org, "S. R. Sudarshan Iyengar"
> 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 + .. +
> 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
> even?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).