A congruence of sum of kth powers of first p-1 numbers
102524
$ 1^k+2^k+3^k+...+(p-1)^k $ always a multiple of $p$?
108318
counting proof for $\sum_{k=0}^{n-1} 2^{k} = 2^n - 1$
6918
Primes congruent to 1 mod 6
101057
Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
112005
Showing that if $p_1 + \cdots p_n = 1$ then $\displaystyle \sum_{k=1}^n \left(p_k + \dfrac {1}{p_k} \right)^2 \ge n^3+2n+\dfrac 1n$?
38727
Modular Exponentiation and Primes
15436
Find p and q s.t. $({p-1})^{q-1}+({q-1})^{p-1} \equiv 101 \pmod {pq}$
54286
Let $p$ a prime number, then prove that : $\sum \limits_{k=0}^{p} \binom {p}{k} \binom{p+k}{k} \equiv 2^p +1 \pmod{p^2}$
26478
Show that the congruence $x^{p-1} \equiv 1 \pmod {p^2}$ has precisely $p-1$ solutions modulo $p^2$
17306
To find all $n$ such that $(n-1)!+1$ is a perfect power of $n$
131708
Sum of powers of natural numbers
75023
A finite sum of prime reciprocals
27585
Combinatorial proof of Stirling Number Identity (First Kind)
9787
Primitive roots modulo primes congruent to n!
140830
Show $\,p\mid 9^q -1 \implies q\mid p-1$ for odd primes $p$ and $q$
52530
There exists a prime congruent to $m$ mod $p$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$