Thread: Sum of powers factorization

Hi everybody,

I think that:



Is factorized in prime numbers (according theorem of arithmetic), that are square free.

In other words its dinstict primes (if multiplied) give as result number N.

i.e.


where


Is this correct?

I think this can be handled with Congruence of Clausen and von Staudt proof. Unfortunatelly i cannot find any link (with proof) into internet.

Thank you a lot

You mean that is always squarefree?

Or does have to be prime?

In any case a counter-example is

Ok counter example is definite thanks

I suggest always checking a couple of cases before conjecturing something, let alone trying to prove it. Counter-examples to your conjecture abound. It took me about three tries to find one.