$S_k \triangleq \sum_{i=1}^{p-1}i^k$ implies $p | S_k$
31184
Sums of powers below a prime
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
4512
Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
154085
$\sum a_i \ln(b_i) \leq \sum a_i \ln(a_i)$ with $\sum a_i = \sum b_i = 1$
108298
Prove $\sum_{i=1}^{i=n}\frac{a_i}{S-a_i}\geqslant \frac{n}{n-1}$ and $\sum_{i=1}^{i=n}\frac{S-a_i}{a_i}\geqslant n(n-1)$.
148458
$x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
46431
Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
81196
Is true that $H^{s,p}(\mathbb{R}^n)\subset C^k(\mathbb{R}^n)$ when $s-k>n/p$?.
111191
Show that $P_i$ and $\sum_i P_i$ being idempotent implies $P_i P_j=\delta_{ij}$
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
66535
How to prove $P(A\cap B)\geqslant P(A)+P(B)-1$?
14197
show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$