Prove that for every positive integer $n, \exists c_n$ such that $f(c_n) = f(c_n+1/n)$
13927
Values of $a$ s.t. for all continuous $f$ with $f(0)=f(1)$ there exists $x$ s.t. $f(x+a) = f(x)$
20909
For each positive integer $n$, let $x_n=1/(n+1)+1/(n+2)+\cdots+1/(2n)$. Prove that the sequence $(x_n)$ converges.
143354
Prove that there exists $c\in\mathbb{R}$ such that $f'(c)=f(c)$
75199
$a \equiv b \pmod n$ and $c\equiv d \pmod n$ implies $ac \equiv bd \pmod n$
90199
Prove that there exists a constant $c>0$ such that the following happens
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
27170
$a\in \mathbb{N}$, $p$ prime, $a<p$ prove that $a\mid p+1\iff\exists\, b,c\in\Bbb N:\dfrac{a}{p}=\dfrac{1}{b}+\dfrac{1}{c}$
145397
How to prove that for every $i$, $a_i = i$
51555
Strictly increasing sequence $\{ a_k \}$ of positive integers such that $\sum 1/{a_k}$ is finite
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
71639
Proof $(1+1/n)^n$ is an increasing sequence
91914
Prove that for the Fibonacci sequence $(F_n)$, $F_n$ divides $F_{2n}$.
104339
Prove that all but finite number of members of sequence are positive if limit is positive
129163
Showing that every positive integer can be represented in this form
28011
Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
139531
If $f'/f=g'/g$ at every $1/n$ then $f=kg$ for some complex number $k$