2004 Indonesia MO Problems/Problem 1
How many odd and even divisors of are there?
We start by factoring the expression. If a divisor is even, then the exponent of the of the divisor’s prime factorization is at least , so there are even divisors.
If a divisor is odd, then the exponent of the of the divisor’s prime factorization is , so there are odd divisors.
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