The number 185136 has the interesting property that it is a triangular number that is also the product of 3 consecutive integers.

I square 185136 and each of the x consecutive numbers following it, and total the sum of all these squares, S.

Then I do the same with 185136+x+1 and the y consecutive numbers following it, until I again reach the same sum, S.

Find positive integer values of x,y,S compliant with the above requirements.

Brian,

If I replace bs in the program listing below with a triangle number where n is even I can recreate the phenomenon.

Exactly. From which observation it should be just a short step to....