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 = 22·3.

If an integer is a square, its prime factors must have even exponents. Thus 12 is not a square, but 36 is (36 = 22·32). 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.