$a^2 \equiv 1 \pmod{311}$
23153
$\bmod p\!:\ x^2\equiv 1\iff x\equiv \pm1\ $ for prime $p$
36043
If $ab \equiv r \pmod{p}$, and $x^2 \equiv a \pmod{p}$ then $y^2 \equiv b \pmod{p}$ for which condition of $r$?
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
74512
How to show $n(n+1)(2n+1) \equiv 0 \pmod 6$?
360
Modular exponentiation by hand ($a^b\bmod c$)
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
109532
Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
144017
How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$
21874
Solve $x^3+x \equiv 1 \pmod p$
38876
$r! \equiv (−1)^k \pmod p$
52530
There exists a prime congruent to $m$ mod $p$
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
66161
How to solve the equation $n^2 \equiv 0 \pmod{584}$?
4129
Solvability of $a \equiv x^2 \mod b$