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.

list
   10      Base=185136
   20      S=Base*Base
   30      for X=1 to 9999
   40        S=S+(Base+X)^2
   50        Sumb=(Base+X+1)^2:Y=0
   60        while Sumb<S
   70          inc Y:Sumb=Sumb+(Base+X+1+Y)^2
   80        wend
   90        if Sumb=S then print X,Y,S
  100      next X
OK
run
 304     303     10471153462280
OK

indicates that x=304, y=303 and S is 10,471,153,462,280.