Legendre Symbol

We are given the prime $p$ and the integers to find the quadratic residue in $p$. The exact values of the prime is given in this link Using Legendre Symbol and Euler’s criterion, a number $a$ can have three cases: $$ (\frac{a}{p}) \equiv a^{\frac{p - 1}{2}} \equiv 1 \text{ if } a \text{ is a quadratic residue and } a \not\equiv 0 \mod p $$ $$ (\frac{a}{p}) \equiv a^{\frac{p - 1}{2}} \equiv -1 \text{ if } a \text{ is a quadratic non-residue } \mod p $$ $$ (\frac{a}{p}) \equiv a^{\frac{p - 1}{2}} \equiv 0 \text{ if } a \equiv 0 \mod p $$ But when the prime is of the form $4k + 3$, then using Euler’s criterion, if a number $a$ indeed has a quadratic residue, then:...