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## Main Question or Discussion Point

how to find the integer solutions of the following equation:

[tex]x^3 + x^{2}y + xy^2 + y^3 = 8(x^2 + xy + y^2 + 1)[/tex]

after simplifying, i got,

[tex](x^2 + y^2)(x + y - 8) = 8(xy + 1)[/tex]

from this, i can see that x and y are both odd or both even. but what should i do next. i tried putting x = 2p and y = 2q but that's not going anywhere.

thanks in advance.

[tex]x^3 + x^{2}y + xy^2 + y^3 = 8(x^2 + xy + y^2 + 1)[/tex]

after simplifying, i got,

[tex](x^2 + y^2)(x + y - 8) = 8(xy + 1)[/tex]

from this, i can see that x and y are both odd or both even. but what should i do next. i tried putting x = 2p and y = 2q but that's not going anywhere.

thanks in advance.