$a_{n+1}=a_{n-1}-{4\over a_n}$ for $n>1$
6874
smallest value of $k$ for which $a_k$ is $0$
62254
Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
133528
$\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$
33495
A limit problem about $a_{n+1}=a_n+\frac{n}{a_n}$
98855
Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
153123
Proving by induction $4^n  0$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
73238
Show that $a^{q-1} \equiv 1 \pmod{pq}$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
88662
$n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer.
97258
Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
103854
Showing that $Q_n=D_n+D_{n-1}$
21781
Prove for any $a>1$ there exist a natural number, $N$, such that $a^n>n$ for all $n \ge N$
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra