Determine the integer solution(s) for (x,y,z) in this system of equations:
**** How fast can you come up with valid solution(s) using only p&p ?.
Most integer solutions to x+y=2 have exactly one of x or y positive and the other negative. In these cases xy-z^2 is strictly negative, and is equated to a positive value, so these cases offer no integer solutions.
That leaves (x,y) = (2,0), (1,1), and (0,2).
If (x,y) = (2,0) or (0,2) then xy-z^2=1 reduces to -z^2=1, which has no integer solutions.
Then finally (x,y)=(1,1) gives us 1-z^2=1, which has one integer solution of z=0.
Then the unique integer solution to the system is (x,y,z)=(1,1,0). This took longer to type than it did to solve.
Solution