Don't look for a certain "algorithm" or anything to study. Very many problems can be solved by ad-hoc analysis and observations and little background knowledge. And this is also the best way to develop as a competitor.

In this particular case, you should look at the factorization of N and assure yourself that all its prime factors are present in the required quantity. The fact that smaller primes appear considerably more often than larger ones in that function might also be of help.

i have tried all what i have to solve this problem

Like what? Please share your thoughts so far...