Show that a is a quadratic residue modulo $p$ iff $ind_{r} (\mathbb{a})$ is even.
59416
Quadratic residues and index w.r.t. primitive root of a odd prime p
77806
Proving if $a$ is not a multiple of prime $p$, then an integer $b$ exists such that $p^b - 1$ is a multiple of $a$
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
29979
When is $-3$ a quadratic residue mod $p$?
60057
number of quadratic residues in finite field
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
60780
Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.
4129
Solvability of $a \equiv x^2 \mod b$
127901
If $x^2+y^2 \equiv 0\pmod{p}$, then $p \equiv 1 \pmod{4}$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
62382
I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
56877
Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
138941
If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p.
108237
Show $a^p \equiv b^p \mod p^2$
94017
If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?