Quadratic non-residues

Number Theory Level 5

Find the smallest $n$ such that for some prime $p$ , at least $20$ of the numbers $1,2,...,n$ are quadratic non-residues modulo $p$ .

Details and assumptions

$k$ is a quadratic residue modulo $p$ if there exists an integer $j$ such that $j^2 \equiv k \pmod{p}$ .

There is no condition on the relative sizes of $n$ and $p$ . As an explicit example, if $p=3$ , then $n=59$ would satisfy the conditions of the question.