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 re(2): a general formula by Charlie)

IMHO  there at least 2 possibilities to generate (x,y,z):  x=n^4*1   creates 17,82,257,626... with y=-z= 2*n^2=8,18,32,50..etc

I LEAVE IT TO THE SOLVERS TO FIND OUT HOW OTHER SOLUTIONS MAY BE GENERATED.

G O O D   L U C K...

 

Posted by Ady TZIDON on 2012-06-03 13:16:25