A note on Linnik's Theorem on quadratic non-residues

Abstract

We present a short, self-contained, and purely combinatorial proof of Linnik's theorem: for any $\epsilon >0$ there exists a constant $C_{\epsilon }$ such that for any $N$, there are at most $C_{\epsilon }$ primes $p⩽N$ such that the least positive quadratic non-residue modulo $p$ exceeds $N^{\epsilon }$.

6 pages