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 Squaring the triangle (Posted on 2013-01-07)

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 No Rating

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 computer solution | Comment 2 of 7 |

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.

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

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