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