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 Some Squares Sum Year (Posted on 2014-01-16)
Each of x, y and z is a positive integer satisfying:
x2+y2+z2 = 2014

How many solutions are there? For which triplets is x+y+z a perfect square? How many distinct values can x+y+z have?

*** Disregard permutations. For example, (p,q,r) and (p,r,q) should be treated as the same solution.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: I can program -- same answers in Basic Comment 2 of 2 |
(In reply to I can program by Jer)

CLS
FOR x = 1 TO SQR(2014 / 3)
FOR y = x TO SQR((2014 - x * x) / 2)
z = INT(SQR(2014 - x * x - y * y) + .5)
IF x * x + y * y + z * z = 2014 THEN
PRINT x; y; z, x + y + z,
sr = INT(SQR(x + y + z) + .5)
IF sr * sr = x + y + z THEN PRINT "*", sr:  ELSE PRINT
END IF
NEXT
NEXT

`             sum ofx   y   z   squares     is square?     square root3  18  41     623  22  39     64           *              85  15  42     625  30  33     689  13  42     64           *              813  18  39    7014  27  33    7418  27  31    7621  22  33    76`

 Posted by Charlie on 2014-01-16 15:53:34

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