2 problems

Let $k\geq 1$ be a natural number, let $a_i$ and $b_i$ be integers for $1\leq i\leq s$, and let $p$ be a prime. A solution $(x_1,\ldots,x_s)\in\mathbb{Q}_p^s$ is non-trivial if it…

Artin's conjecture. Such a system has a non-trivial $p$-adic solution for every prime $p$ whenever