Each integer has a unique prime factorization (a way of expressing
the number as a product of primes, integers that have no divisors
other than themselves and 1). For example,
If an integer is a square, its prime factors must have even exponents.
Thus 12 is not a square, but 36 is
Try finding the smallest positive n that satisfies the first two conditions in order to get a feeling for how the puzzle can be solved.