Show that $\{\frac{f_k}{n}\}$ undergoes a cycle, where $\{M\}$ is the fractional part of $M$ and $f_k$ is the $k^\text{th}$ Fibo number
111822
Is it true that the Fibonacci sequence has the remainders when divided by 3 repeating?
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
84823
When is the group of units in $\mathbb{Z}_n$ cyclic?
106502
Prove by induction that for the Fibonacci numbers $F(n)$ with $n \ge 6$, $F(n) \ge 2^{n/2}$
14210
Fibonacci divisibilty properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$
83036
f(g(x)) has a degree divisible by n
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
20574
Understanding the proof for $\gcd (F_n, F_{n+k}) = 1$ where $F_n$ is a Fermat number
152653
Count Eulerian cycles in $K_{n,2}$
151111
How do I show that $\frac{n}{\varphi(n)}=\sum\limits_{d \mid n} \frac{\mu^2(d)}{\varphi(d)}$?
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
48610
Fibonacci Numbers Proof: $ f_n = \binom n0 + \binom{n-1}1 +\dots+ \binom{n-k}k$
78319
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
67886
How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence
155066
Dimension of the quotient space $\frac{C_{0}}{M}.$
68400
Proof that $\frac{(2n)!}{2^n}$ is integer