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 Partly solved by Jer)

For your expression of S, S^2 + 15^2 is the square of an expression:

(30ab/(a^2 - b^2))^2 + 15^2

= 15^2( 2ab/(a^2-b^2) + 15^2

= (15(a^2+b^2)/(a^2-b^2))^2........(*)

Edited on March 29, 2007, 12:56 pm

Posted by K Sengupta on 2007-03-29 11:51:48