Problem 136

Singleton difference

The positive integers, *x*, *y*, and *z*, are consecutive terms of an arithmetic progression. Given that *n* is a positive integer, the equation, *x*^{2}*y*^{2}*z*^{2} = *n*, has exactly one solution when *n* = 20:

13^{2} 10^{2} 7^{2} = 20

In fact there are twenty-five values of *n* below one hundred for which the equation has a unique solution.

How many values of *n* less than fifty million have exactly one solution?

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