Let $a_1=1$ and $a_n=n(a_{n-1}+1)$ for $n=2,3,...$.
137702
How I find limit of $P_n$
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
107098
Find an explicit formula for the recurrence $a_n = n(a_{n-1} + a_{n-2})$ knowing that $ a_0=1$ and $a_1=2$.
56311
Proving $(1+a_{2})^{2}(1+a_{3})^{3}\cdots(1+a_{n})^{n}\ge n^n$ for positive reals $a_2,\ldots, a_n$ whose product is $1$
51706
If $(k,l) = 1$, show that $(b_2k-b_1l, a_1l-a_2k) = 1$ for $a_1b_2-a_2b_1=1$
144890
Recurrence $f_{n+2}=af_{n+1}+bf_n$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
59036
If $a^{n}-1$ is prime then $a=2$ and $n$ is prime?
135018
Proving that a sequence has $a_n = a_{n+2}$ for $n$ sufficiently large.
42780
Show that if $a^{n-1} \equiv 1 \pmod{n}$ for all $a$ such that $\gcd(n,a) = 1$, then $a^{n} \equiv a \pmod{n}$ for all $a$.
103854
Showing that $Q_n=D_n+D_{n-1}$
139074
Question about $a_n=\sum_{k=1}^n \frac{n}{n^2+k}\ $for $ n \in\mathbb{N}$
94580
Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$
25583
Show that the sequence $a_0 = 1$, $a_{n+1 }= \sqrt{2+a_n}$ is monotonically increasing
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
91105
For every $n\ge3$ there exists $n$ different integers $a_1,...,a_n$ so that $\frac{1}{a_1}+\frac{1}{a_2}+...+\frac{1}{a_n}=1$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$