2 problems

Let $x_1,\ldots,x_r$ be roots of unity and let $a\in\mathbb{C}\setminus\mathbb{Z}$. For $\boldsymbol{k}=(k_1,\ldots,k_r)\in\mathbb{N}^r$ with $(k_1,x_1)\neq(1,1)$ and…

Let $r>1$, let $x_1,\ldots,x_r$ be roots of unity, let $a\in\mathbb{C}\setminus\mathbb{Z}$, and let $k_1,\ldots,k_r\geq1$ with $(k_r,x_r)\neq(1,1)$. Parity conjecture. The combinat…