设 x+y+z+w=C,这样 xy+z+w-C+1= (x-1)(y-1) = 51-C
同理 (y-1)(z-1) = 91-C, (z-1)(w-1)=185-C,(w-1)(x-1) = 2025-C
所以 (91-C)(2025-C) = (51-C)(185-C)
解出 C= 174840÷1880= 93
所以 (x-1)(y-1)= -42, (y-1)(z-1)=-2, (z-1)(w-1)=92, (w-1)(x-1)=1932
x-1= 21(z-1),w-1=92/(z-1), y-1= -2/(z-1)
代进(x-1)+(y-1)+(z-1)+(w-1)= 89
21(z-1)-2/(z-1)+(z-1)+92/(z-1)= 22(z-1)+90/(z-1) = 89
z-1= 2 或 45/22
最后解出来 x=43, y=0, z=3, w=47 或者 x=967/22, y=1/45, z=67/22, w=2069/45