Suppose $p$ is an odd prime. Show that $1^{p-1} +2^{p-1}+ \ldots +(p-1)^{p-1}\equiv -1\pmod p$
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
92416
About a sum of Legendre symbols associated to an odd prime
123033
Showing a number $n$ is prime if $(n-2)! \equiv 1 \pmod n$
51858
Showing $\gcd(2^m-1,2^n+1)=1$
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
154933
Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
52644
Prove $2^k+1$ divisible by 3 for odd K
37093
If p is an odd prime, prove that $1^2 \times 3^2 \times 5^2 \cdots  \times (p-2)^2 \equiv (-1)^{(p+1)/2}\pmod{p}$
157884
For any prime $p>3$ show that 3 divides $2p^2+1$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
54359
Odd Primes Problem Proof
86594
If $x^2 \equiv y^2 \pmod {p^r}$, where $p$ is an odd prime not dividing $x$ or $y$ then $x \equiv \pm y \pmod {p^r}$
140948
Suppose $p$ and $q$ are odd primes and $p = q + 4a$ for some $a$. Prove that $(\frac ap) = (\frac aq)$ holds.
21250
Prove $x \equiv a \pmod{p}$ and $x \equiv a \pmod{q}$ then $x \equiv a\pmod{pq}$
98871
How to prove that if a prime divides a Fermat Number then $p=k\cdot 2^{n+2}+1$?
60305
Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$