Problem 2 Given x^5=1 and x \neq 1, find a = \left( {1 \over x^2+x+1} + {1 \over x^2-x+1} \right)^5 I posted an answer on Twitter/X, here. Solution here, which also discusses generalising to other roots of unity (i.e. x^n=1, x \neq 1).