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 Four special natural numbers (Posted on 2008-12-11)
Find all sets of four natural numbers such that the square of each of them, when added to the sum of the other three, again yields a perfect square.

 See The Solution Submitted by pcbouhid No Rating

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 computer exploration--is there a pattern to this? | Comment 6 of 8 |
1  1  1  1
1  5  5  5
1  8  8  8
6  6  11  11
1  16  16  16
1  21  21  21
1  33  33  33
1  40  40  40
1  56  56  56
1  65  65  65
1  85  85  85
1  96  96  96
40  57  96  96
1  120  120  120
1  133  133  133
1  161  161  161
1  176  176  176

DEFDBL A-Z
CLS
FOR t = 4 TO 612
FOR a = 1 TO t / 4
FOR b = a TO (t - a) / 3
FOR c = b TO (t - a - b) / 2
d = t - a - b - c
good = 1
sq = a * a + b + c + d
sr = INT(SQR(sq) + .5)
IF sr * sr = sq THEN
sq = a + b * b + c + d
sr = INT(SQR(sq) + .5)
IF sr * sr = sq THEN
sq = a + b + c * c + d
sr = INT(SQR(sq) + .5)
IF sr * sr = sq THEN
sq = a + b + c + d * d
sr = INT(SQR(sq) + .5)
IF sr * sr = sq THEN
PRINT a; b; c; d
END IF
END IF
END IF
END IF

NEXT
NEXT
NEXT
NEXT

 Posted by Charlie on 2008-12-12 00:17:29

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