I was trying to figure out the remiander when $(a+b+c)^{333}-a^{333}-b^{333}-c^{333}$ is devided by $(a+b+c)^3-a^3-b^3-c^3$.
I first tried to factor them but this guy don't factor in any nice way. I don't know much number theory. I think moduler arithmetic might help. But I don't know that properly either. Can some one please help me out?