Find x,y,z in Z solutions for system :
Let
Then
Replace s in the second equation. Then . The quadratic equation having the roots such as their sum is s and their product is p is
That means . The roots of this equation are x and y and are integers. Then the discriminant must be a perfect square.
Replace z in t-equation: with the roots 13 and 78. So, or
You can try other cases:
or etc.