Congruence in the solutions of an expression $ax\equiv b \pmod{n}$
32463
$ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$
45882
Solving a congruence without Fermat's little theorem
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
22962
How to show $\binom{2p}{p} \equiv 2\pmod p$?
15314
Number of solutions to $x^n \equiv 1 \mod p$
121717
Prove that $z^2 \equiv ab\pmod p$ is solvable if and only if both or neither of $x^2 \equiv a \pmod p$, $x^2 \equiv b \pmod p$ are solvable.
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
89590
The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
21874
Solve $x^3+x \equiv 1 \pmod p$
52530
There exists a prime congruent to $m$ mod $p$
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
80875
Congruence equation ...
2904
Solving linear congruence (modular inverse or fraction) via gcd Bezout equation
108035
solving diophantine equations using congruences
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
96237
$1^2 + 2^2 + 3^2 + \cdots + (n-1)^2 \equiv 0$ mod n iff $n \equiv \pm 1$ mod 6
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.