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lets consider the prime factorisation of a number N let the powers of the primes in this factorisation be a,b,c ....and so on. Is there a way to determine whether the number of powers that are even are greater than the odd ones or not.the factorisation is not known

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I guess you assume the factorisation is not known? Otherwise you simply count. – gammatester Oct 28 '13 at 14:44
yes its not known – user103260 Oct 28 '13 at 14:52
I believe it's impossible to do this, for general numbers $N$, with any less effort than factoring the number anyway. – Greg Martin May 10 '15 at 18:40

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