Prove that there are as many quadratic residues mod p as there are quadratic non-residues mod p
60780
Help needed in understanding proof: Every odd prime $p$ has exactly $(p-1)/2$ quadratic residues and $(p-1)/2$ quadratic nonresidues.
94917
Prove that for every prime $p$, there exists a solution to $(x^2-2)(x^2-6)(x^2-3) \equiv 0 \mod(p)$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
4129
Solvability of $a \equiv x^2 \mod b$
17176
Proof that $x^n \mod b = (x \mod b)^n$
120627
Reducibility of polynomials modulo p
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
93820
Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
130300
Proof that every quadratic residue has two roots, modulo a prime
103499
$x^2 \equiv a \mod p$, $\ x^2 \equiv b \mod p$, and $x^2 \equiv ab \mod p$, prove either all three are solvable or exactly one
138941
If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p.
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
136367
Prove $ ∀a, b, c ∈ Z,$ if $ab + ac ≡ 3$ (mod 6) then b $\not\equiv$ c (mod 6).
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
105225
Number Theory: Complete set of residues modulo $n$
51153
Number of solutions to $x^2\equiv a\pmod m$