Counting the solutions of ${\lambda }_1{x}_1^{k_1}+\cdots +{\lambda }_t{x}_t^{k_t}\equiv c\mathrm{mod}n$

Songsong Li, Yi Ouyang

Given a polynomial $Q(x_1,\cdots ,x_t)={\lambda }_1{x}_1^{k_1}+\cdots +{\lambda }_t{x}_t^{k_t}$, for every $c\in \mathbb{Z}$ and $n\ge 2$, we study the number of solutions $N_J(Q;c,n)$ of the congrue…