Many interesting Diophantine geometry problems involve finding integral points on affine surfaces, for example the sum of three cubes problem which states: For n in Z, not congruent to 4 or 5 mod 9 the affine surface
u_1^3+u_2^3+u_3^3=n in A^3_Z (1)
always has an integral point. Colliot-Thélène and Wittenberg showed that the affine surface (1) has no integral Brauer-Manin obstruction for any choice of n in Z. Building on the work of Colliot-Thélène and Wittenberg, I will show the affine surfaces f(u_1)+f(u_2)+f(u_3)=n in A^3_Z have no integral Brauer-Manin obstruction for all but finitely many n in Z. | 
