Find the product $(1-a_1)(1-a_2)(1-a_3)(1-a_4)(1-a_5)(1-a_6)$ Let $1,$ $a_i$ for $1 \leq i \leq 6$ be the different roots of $x^7-1$.
Then find the product:
$(1-a_1)(1-a_2)(1-a_3)(1-a_4)(1-a_5)(1-a_6)$
I don't know how to proceed.

Hint.  Factorising,
$$x^7-1=(x-1)(x-a_1)\cdots(x-a_6)\ .$$
Dividing by $x-1$ gives
$$x^6+x^5+\cdots+1=(x-a_1)\cdots(x-a_6)\ .$$
I'm sure you can finish the problem from here.
