You mean that is always squarefree?
Or does have to be prime?
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.
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