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.
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
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Posted by Charlie
on 2008-12-12 00:17:29 |
computer exploration--is there a pattern to this?
