## Puzzle: for first years only

Here is a puzzle for 1st years only (i.e. prize only to a 1st year student if solved correctly).

Suppose $a+b=1$ and $a^3+b^3=1$. What then is $a^{17}+b^{17}$? (There is a very fetching way of solving this by Gröbner bases.)

(MG)