Show that there can only be finitely many numbers $n \in \mathbb{N}$ for which $f(1/n) = 1/(n + 1)$.
112512
How to prove that there are finitely many $n$ such that $f(1+1/n) = \frac{1}{n+1}$?
18950
Show that $f$ has at most one fixed point
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
76977
Prove that $f(n)$ is the nearest integer to $\frac12(1+\sqrt2)^{n+1}$?
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
138026
To show that $n!f(x) \in \mathbb{Z}[x]$
144787
Show that the set of all infinite subsets of $\mathbb{N}$ has cardinality greater than $\mathbb{N}$
59535
Prove that there exists such a set of $n$ positive integers
21431
The set of all functions from $\mathbb{N} \to \{0, 1\}$ is uncountable?
104016
Limit point of the set $G= \{1/n: n \in \mathbb N\}$?
31889
The limit as $n$ approaches infinity of $n(a^{1/n}-1)$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
58663
How to show that if $\phi(n)$ equals to n itself, then n must be 1?