2 problems

Let $p$ be an odd prime, let $H=\langle-1,2\rangle\subset\mathbb{F}_p^{\times}$, let $\ell_0$ be the index parameter used for $H$, and let $g$ be a generator of…

Let $d_1,\dots,d_s$ be the exponents of a diagonal equation, and suppose there is a bound for the number of its solutions with restricted coordinates, explicitly expressed in terms…