Consider three positive integers x< y< z in

Harmonic Sequence.

Determine all possible values of the positive integer constant S for which the equation 15x + Sy = 15z admits of valid solutions.

(In reply to

a few found by brute force.... by Dej Mar)

1. Looking at the evaluated values it seems that 8^2 + 15^2 = 17^2; 20^2 + 15^2= 25^2, and so on.

So, S^2 + 15^2 appears to be a perfect square for these values of S. (Why?)

2. Since S must be a positive integer, the value S=0 is not valid.