Definition of quadratic residues in $\mathbb{F}_q$, where $q = p^n$.
60057
number of quadratic residues in finite field
29979
When is $-3$ a quadratic residue mod $p$?
27942
showing that $n$th cyclotomic polynomial $\Phi_n(x)$ is irreducible over $\mathbb{Q}$
140198
Let $a$ be a quadratic residue modulo $p$. Prove that the number $b\equiv a^\frac{p+1}{4} \mod p$ has the property that $b^2\equiv a \mod p$.
130499
How can $p^{q+1}+q^{p+1}$ be a perfect square?
153869
Under what $p$, $-1$ is a square in $\mathbf F_p$?
122932
When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?
68635
When is $2$ a quadratic residue mod $p$?
116686
$p=2^n+1$. Prove that every quadratic nonresidue modulo $p$ is a primitive root modulo $p$
24168
A characterisation of quadratic extensions contained in cyclic extensions of degree 4
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
55764
Algebraic closure of $\mathbb F_p$
84017
Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
134701
Polynomials irreducible over $\mathbb{Q}$ but reducible over $\mathbb{F}_p$ for every prime $p$
4706
Prove $f=x^p-a$ either irreducible or has a root. (arbitrary characteristic) (without using the field norm)
134619
Galois extension with $X^4-2aX^2+b\in\mathbb Q[X]$
103561
Residue fields of schemes of finite type (over $\mathbb{Z}$)