I have a pretty difficult math question that I have no idea even how to begin. Here it goes:
Find the nonzero integers $a$, $b$, $c$ such that $a^3 + b^3 + c^3 = 2$?
I would assume that at least one of the integers would be negative. Also, I got as far as $(a+b+c)^3 = 2^3$ but I'm not sure what good this will do.
(So, not to cower in shame I made a mistake above seeing as how $(a+b+c)^3 \ne 2^3$. I admit I failed there. But how to work this equation?)