Problem 919

Using Euler's criterion, we can obtain the following conclusions:
(1) -1 is a quadratic residue of primes of the form $4 k+1$, and a quadratic non-residue of primes of the form $4 k+3$.
(2) If $a_{1}, a_{2}$ are both quadratic residues modulo $p$, then $a_{1} a_{2}$ is a quadratic residue modulo $p$; if $b_{1}, b_{2}$ are both quadratic non-residues modulo $p$, then $b_{1} b_{2}$ is a quadratic residue modulo $p$; if $a_{1}$ is a quadratic residue modulo $p$ and $b_{1}$ is a quadratic non-residue, then $a_{1} b_{1}$ is a quadratic non-residue modulo $p$.