Quadratic residues, mod 5, non-residues mod p 1) If $p\equiv 1\pmod 5$, how can I prove/show that 5 is a quadratic residue mod p?
2) If $p\equiv 2\pmod 5$, how can is prove/show that 5 is a nonresidue(quadratic) mod p?

1)  $(5/p) = (p/5)$ since $p$ is $1(mod 5)$ then $(p/5) = (1/5) = 1$. So 5 is a quadratic residue mod p.
2) again $(5/p) = (p/5)$ since $p$ is $2(mod5)$ then $(p/5) = (2/5) = -1$ since 5 is 5(mod8). So 5 is not a quadratic residue
