If $a_{1}=1$ and $a_{2} = 2,$ and $a_{n}=a_{n-1}+a_{n-2},$ Then $a_{n}$
64328
How to prove that the Binet formula gives the terms of the Fibonacci Sequence?
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
144260
Solve recurrence relation $a_n = 3 a_{n - 3} + a_{n-1} + 2 n$
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
107824
Proof by induction that $a_0 = 1, a_1 = 1, a_n=2a_{n-1} + 3a_{n-2}$ satisfies $a_n = \frac12 (3^n) + \frac12 (-1)^n$
5708
Prove that if $k\ge 1\,$ and $\,a^k\equiv 1\pmod{\! n}$ then $\gcd(a,n)=1$
7091
If $\gcd(a,b)=1$, then $\gcd(a^n,b^n)=1$
89175
Proof of $(a+b)^{n+1}$
158862
Show that $a(-1) = (-1)a = -a $.
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
62382
I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
99782
$a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
78575
If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
73391
Prove that if $\gcd(a,b)=1$, then $\gcd(a^2,b^2)=1$
70827
Prove that $\sum_{i = n - b}^{a - m} {a - i \choose m}{b + i \choose n} = {a + b + 1 \choose m + n + 1}$