Factorize as: (x+y+1)(x²+y²+1-xy-x-y)=p x+y+1>1, so x+y+1=p then x²+y²+1-xy-x-y=1 x²-x(y+1)+y²-y=0 By checking discriminant, easy to find that y<3. Now, just check all cases (x,y)=(2,2)