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

How many primes p are there such that:

equation

is a perfect square?

Since the expression:

equation

is odd, the perfect square in question must also be odd:

equation

After algebraic manipulation:

equation

equation

equation

equation

equation

and the possibilities for obtaining a product of two consecutive positive integers are:

equation

equation

equation

Therefore, there are three possible primes that satisfy the equation.