Originally Posted by

**johnsy123** I am having troubles with the following questions.

1) Find three numbers such their sum is a square and the sum of any pair is a square?

I set up 4 equations but couldn't solve them....

-a+b+c=d^2

-a+c=f^2

-a+b=e^2

-b+c=h^2

how would i go about this?

Let :

$\displaystyle \begin{cases}x+y+z=a^2 \\x+y=b^2 \\x+z=c^2 \\y+z=d^2\end{cases}$

then :

$\displaystyle 2a^2=b^2+c^2+d^2$

There is an infinite number of triples (x,y,z) which represents solution .

This Maple program calculates triples (x,y,z)

Code:

for a from 0 to 20 do
for b from 0 to 20 do
for c from 0 to 20 do
for d from 0 to 20 do
if 2*a^2=b^2+c^2+d^2 then
print(solve({x+y=b^2, x+z = c^2, y+z=d^2}, [x, y, z]));
end if;
end do;
end do;
end do;
end do;