Number of solutions to $x^{k}\equiv 1\pmod {p}$
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
151764
modular arithmetic, solving $ax + b \equiv c \pmod d$?
130342
Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
89590
The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
18634
Combinations of sets raised to the power of a prime modulus: $\binom{p^{\alpha}-1}k \equiv (-1)^k \pmod p$
126820
How many positive integer solutions are there to the equality $x_1+x_2+...+x_r= n$?
99264
the number of positive-integer solutions that satisfy $x_1\cdot x_2\cdot x_3\cdot x_4=1,000,000$?
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
74512
How to show $n(n+1)(2n+1) \equiv 0 \pmod 6$?
39993
Count the number of positive solutions for a linear diophantine equation
144017
How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$
32463
$ax\equiv b\pmod{\! n}$ has a unique solution if $\gcd(a,n) = 1$
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
135465
Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
112390
Solutions of $x^2 \equiv 1 \pmod N$