Problem 135

Same differences

Given the positive integers, *x*, *y*, and *z*, are consecutive terms of an arithmetic progression, the least value of the positive integer, *n*, for which the equation, *x*^{2}*y*^{2}*z*^{2} = *n*, has exactly two solutions is *n* = 27:

34^{2} 27^{2} 20^{2} = 12^{2} 9^{2} 6^{2} = 27

It turns out that *n* = 1155 is the least value which has exactly ten solutions.

How many values of *n* less than one million have exactly ten distinct solutions?

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