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 Four special squares (Posted on 2014-01-30)
There are only four squares that are equal to the sum of three consecutive cubes.

Zero is one of them.

Find the other three.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solution | Comment 3 of 5 |

DEFDBL A-Z
CLS
cu = 0: p = -1: pp = -8: sum = -9
FOR i = 1 TO 99999
ppp = pp: pp = p: p = cu
cu = i * i * i
sum = sum + cu - ppp
sr = INT(SQR(sum) + .5)
IF sr * sr = sum THEN
PRINT pp; p; cu, sum; sr
PRINT i - 2; i - 1; i
PRINT
END IF
NEXT i

reports

`-1  0  1                     0  0-1  0  1`
` 0  1  8                     9  3 0  1  2`
` 1  8  27                    36  6 1  2  3`
` 12167  13824  15625         41616  204 23  24  25 `

indicating the desired numbers are 0, 9, 36 and 41616.

The first line of each set contains the three cubes to be added, followed by the resulting square and its square root.

The second line in each contains the bases of the cubes, that is, the cube roots of the respective cubes.

 Posted by Charlie on 2014-01-30 18:51:01

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