Let $p$ be a prime. Compute $1^k + 2^k + \ldots + (p-1)^k \pmod{p}$.
152
What is $1^k+2^k+\cdots+ (p-1)^k$ modulo $p$? (From Ireland and Rosen).
58182
How to prove that $\mathbb{Q}[\sqrt{p_1}, \sqrt{p_2}, \ldots,\sqrt{p_n} ] = \mathbb{Q}[\sqrt{p_1}+ \sqrt{p_2}+\cdots + \sqrt{p_n}]$, for $p_i$ prime?
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
119657
If $ f _p(x)=1+x+x^2+ \cdots +x^{p-1} $ where $p$ is prime number, $e$ is any positive integer.
66851
If $p,q$ are primes $(pq,a)=1$ and $p-1|q-1$ then prove $a^{q-1}\equiv 1\pmod{pq}$
120554
highest power of prime $p$ dividing $\binom{m+n}{n}$
3109
Prove that $(p+q)^m \leq p^m+q^m$
14724
For primes $p≡3\pmod 4$, prove that $[(p−1)/2]!≡±1\pmod p$.
130615
divisibility of binomial coefficients by primes
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
151961
Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
62382
I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
31184
Sums of powers below a prime
42885
Fermat primes relation to $2^n+1$
20980
Prove that $\frac{p^p-1}{p-1}$ is not prime if $p \equiv 1 \pmod 4$
156607
Show that $L_p =\frac{1^p+2^p+3^p+...+(p-1)^p}{p}$ is an integer and generalize the integer for all odd integers p
151036
arithmetic progression of primes