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 12²⁰?

(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 12²⁰?

This is a typographical anomaly which is regretted.

Posted by K Sengupta on 2014-11-23 00:09:28