Find ALL integer solutions of
x*y*z=x+y+z.

Same question if non-integer solutions are accepted.

For ( x, y, z) the integer solutions for x*y*z = x+y+z are:

( 0, 0, 0), ( 1, 2, 3), ( 1, 3, 2), ( 2, 1, 3), ( 2, 3, 1), ( 3, 1, 2),
( 3, 2, 1), (-1,-2,-3), (-1,-3,-2), (-2,-1,-3), (-2,-3,-1), (-3,-1,-2), (-3,-2,-1),
and where a is any positive integer:
( 0,-a, a), ( 0, a,-a), (-a, 0, a), (-a, a, 0), ( a, 0,-a), ( a,-a, 0)

 

Posted by Dej Mar on 2013-04-04 10:39:58