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Squaring the triangle (Posted on 2013-01-07) Difficulty: 3 of 5

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.

See The Solution Submitted by broll    
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Solution computer solution | Comment 2 of 7 |

   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
 304     303     10471153462280

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

  Posted by Charlie on 2013-01-07 18:10:56
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