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.

Because x < y < z are in Harmonic sequence: a, b, c, the equation can be rewritten as
S = [3 * 5 * (c² - a²)] / [2 * (a * c)].
Because S, x, y and z are positive integers, all valid solutions for S must be where 3 * 5 * (c² - a²) includes all the factors that comprise 2 * (a*c). 

 

Edited on March 29, 2007, 8:14 pm

Posted by Dej Mar on 2007-03-29 18:19:45