$x ≡ a \pmod{m}, x ≡ b\pmod{n}, x ≡ c\pmod{r}$
32544
Give an example of three positive integers m, n, and r
55621
Show that if $c_1, c_2, \ldots, c_{\phi(m)}$ is a reduced residue system modulo m, $m \neq 2$ then $c_1 + \cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
978
Solving $ax \equiv c \pmod b$ efficiently when $a,b$ are not coprime
14809
Existence & uniqueness of solutions of linear congruences $\ cx\equiv b\pmod m$
60804
About the property of $m$: if $n < m$ is co-prime to $m$, then $n$ is prime
30630
Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
72551
Proof that $\rho = \pm1$ implies linear combination
61825
Congruence class $[a]$ modulo $m$, $\gcd(x, m) = \gcd(a, m)$
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
17176
Proof that $x^n \mod b = (x \mod b)^n$
77064
Proving $\gcd((a+b)^m,(a-b)^m)\le2^m$ for coprime $a,b$ and $m \in \Bbb N$
47232
Prove $\forall a,b,c \in \mathbb Z$, if $ab+ac\equiv 3\pmod 6$ then $b \not\equiv c \pmod 6$ by contraposition
90438
To prove that if $ab\equiv ac\bmod n$ and $(a,n)=1$ then $b\equiv c\bmod n$
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$