Find three distinct integers, X, Y and Z, such that X + Y, X + Z, Y + Z, X - Y, X - Z, and Y - Z are all squares of integers.
Apparently, there are many solutions.

Find the set [X, Y, Z] with the smallest X + Y + Z.

(In reply to aha -- computer solution by Charlie)

Ah yes.

The time I wasted on this, before I worked out the trick!

x is 17, y is 8, z is -8; x+y+z=17.

The problem with distinct positive integers {x,y,z} is interesting though and might be worth another problem....

Edited on June 2, 2012, 4:19 pm

Posted by broll on 2012-06-02 15:58:59