Small solutions to inhomogeneous and homogeneous quadratic congruences modulo prime powers

Stephan Baier, Arkaprava Bhandari, Anup Haldar

We prove asymptotic formulae for small weighted solutions of quadratic congruences of the form $\hat{I}{»}_1{x}_1^2+\cdots +\hat{I}{»}_n{x}_n^2\equiv \hat{I}{»}_{n+1}\mathrm{mod}{p}^m$, where $p$ is a fixed odd prim…