Show that $16$ is a perfect $8$th power modulo $p$ for any prime number $p$
31064
Showing $x^8\equiv 16 \pmod{p}$ is solvable for all primes $p$
25428
Prime numbers of the form $ n^{34} -9$
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
6160
How to prove a number $a$ is quadratic residue modulo $n$?
5206
Highest power of a prime $p$ dividing $N!$
58935
If $p$ and $p^2+8$ are both prime numbers, then $p^3+4$ is prime.
71788
Prove existence of multiplicative inverse modulo p when p is prime
121890
Proof that $ p $ | ${ p^n \choose k } $ for any prime $p$ and $ k < p^n$
21108
Perfect squares and modularly congruency in mod 5
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
41925
What is the distribution of primes modulo $n$?
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
14724
For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
51445
Number Theory: Find all solutions of $\phi(n)=16$ and $\phi(n)=24$
131476
consecutive prime power
28957
Verifying that $2^{44}-1$ is divisible by $89$