n and k are natural numbers, k is odd

Prove that( 1 + 2 + 3 + ... + n )is a factor of( 1)^{k}+ 2^{k}+ 3^{k}+ ... + n^{k}

I start the proof by using mathematical induction ( but don't know how to do it ), then I try to tackle from a special case :

[ e.g. The case( 1 + 2 )is a factor of( 1where k is natural and odd --- I can proof it but do not know how to extend it ]^{k}+ 2^{k})

Can anyone give me a suggestion ( Better be simple because I am not good at math. )

** This is not a homework. I saw this question on another web site ( not a math. forum ) 2 days ago.

I thought it was an easy question so I have spent the past 2 days to solve it. ( It seems I was overly confident )