Show that the congruence equation $x^8 \equiv 16 \pmod p$ has a solution for every prime $p$.
31064
Showing $x^8\equiv 16 \pmod{p}$ is solvable for all primes $p$
61825
Congruence class $[a]$ modulo $m$, $\gcd(x, m) = \gcd(a, m)$
80843
Find all solutions to $x^9 \equiv 25 \pmod {29}$
32762
Proof for: $(a+b)^{p} \equiv a^p + b^p \pmod p$
89590
The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
123441
Quadratic congruences problem $(x^2-a)(x^2-b)(x^2-ab)$ ≡ 0 (mod p)
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
127945
Number of solutions to the congruence $x^q \equiv 1 \mod p$.
124995
$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
15314
Number of solutions to $x^n \equiv 1 \mod p$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
7414
Prove that odd perfect square is congruent to $1$ modulo $8$
46028
Show that the solution for the Diophantine equation $x^2 - y^2 = N$ is unique if and only if $|N|$ or $\frac{|N|}{4}$, respectively, is $1$ or prime.
75318
How do you prove that a prime is the sum of two squares iff it is congruent to 1 mod 4?
69858
Congruence Equation $3n^3+12n^2+13n+2\equiv0,\pmod{2\times3\times5}$
126725
If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...