For how many ordered pairs (x,y,z) of positive integers with x < y < z is the harmonic mean of x, y and z equal to 12^{20}?

(In reply to

Question by Ady TZIDON)

The word *pairs* inclusive of the problem text should have been **triplets**,** **and the problem text should read as follows:

*For how many ordered triplets (x,y,z) of positive integers with x < y < z is the harmonic mean of x, y and z equal to 12*^{20}?

This is a typographical anomaly which is regretted.