The distribution of quadratic residues and nonresidues in arithmetic progressions

We prove some results concerning the distribution of quadratic residues and nonresidues in arithmetic progressions in the setting \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ {{\mathbb{F}}_p}={{\mathbb{Z}} \left/ {{p\mathbb{Z}}} \right.} $\end{document}, where p is a large prime.