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Let $\mathcal{A}$ denote a finite set of arithmetic progressions of positiveintegers and let $s \geq 2$ be an integer. If the cardinality of $\mathcal{A}$is at least 2 and $U$ is the union formed by taking certain arithmeticprogressions of length $s$ from each element of $\mathcal{A}$, we calculate theasymptotic density of the set of all prime numbers $p$ such that $U$ is a setof quadratic residues (respectively, quadratic non-residues) of $p$.

On the density of primes with a set of quadratic residues or non-residues in given arithmetic progression