# Puzzle of the Week for 5 April 1999: Hints

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,
12 = 2^{2}·3.

If an integer is a square, its prime factors must have even exponents.
Thus 12 is not a square, but 36 is
(36 = 2^{2}·3^{2}).
Similarly, if an integer is a cube, its prime factors must have exponents
that are divisible by 3.

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.

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