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.