the easy part is x=y and needs no explaining
This simplifies the problem to find the integer solutions of x^{2}+y^{2}+xy3x3y=0 or y^{2}+(x3)y+x^{2}3x=0
Wich has two solutions:
y=(x+3+sqrt((x3)^{2}4(x^{2}3x)))/2
and
y=(x+3+sqrt((x3)^{2}4(x^{2}3x)))/2
the determinant must be positive, thus (x3)^{2}4(x^{2}3x)=3x^{2}+2x+3 >= 0
Which implies that x is bounded by 1 and 3
The integer solutions are {1,2}, {0,3}, {2,1} and {3,0} and of course the solution [0,0]
I must learn to use tex :(
Last fiddled with by S485122 on 20061029 at 16:17
