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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

How many integers x are there such that:

equation

is a perfect square?

Factoring into primes:

equation

we need to divide this number such as to have only prime factors at even powers as a quotient. For example:

equation

The numbers x that satisfy form the set:

equation

There are 4 such numbers.