Show that infinitely many positive integer pairs $(m,n)$ exist s.t $\frac{m+1}{n}+\frac{n+1}{m} \in \mathbb{N}$
33810
Proving there are an infinite number of pairs of positive integers $(m,n)$ such that $\frac{m+1}{n}+\frac{n+1}{m}$ is a positive integer
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
90076
Prove that every positive integer $n$ is a unique product of a square and a squarefree number
112512
How to prove that there are finitely many $n$ such that $f(1+1/n) = \frac{1}{n+1}$?
115258
Find all positive integers $n$ such that $\phi(n)+\sigma(n)=2n$.
22367
How do I prove that for every positive integer $n$, there exist $n$ consecutive positive integers, each of which is composite?
4061
Proving there are infinitely many pairs of square-full consecutive integers
135955
Prove: The positive integers cannot be partitioned into arithmetic sequences (using Complex Analysis)
148796
Calculating $\tau(n)$, the number of positive divisors of $n \in \mathbb N$
79767
Properties of $x_k=\frac{a_{k+1}-a_{k}}{a_{k+1}}$ where $\{a_n\}$ is unbounded, strictly increasing sequence of positive reals
71108
Is there an integer $N>0$ such that $\varphi(n) = N$ has infinitely many solutions?
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
56574
For any integer $a,b$ let $N_{a,b}$ denote the number of positive integer $x<1000$ satisfying $x= a( mod\;27)$ and $x=b(mod\;37)$. Then
135892
Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes
5142
Infinitely many primes of the form $pn+1$
112182
Sequence of positive integers such that their reciprocals are in arithmetic progression
8446
Number of solutions over positive integers of $x_1 + x_2 + ... + x_n = S$ for $x_i \in [0, 25]$