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.

(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 of
x   y   z   squares     is square?     square root
3  18  41     62
3  22  39     64           *              8
5  15  42     62
5  30  33     68
9  13  42     64           *              8
13  18  39    70
14  27  33    74
18  27  31    76
21  22  33    76

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