Are $1$ and $3$ the only numbers of the form $2^n-1$ that exist in the Fibonacci sequence?
62565
Prove: the intersection of Fibonacci sequence and Mersenne sequence is just $\{1,3\}$
119891
Divisibility and the Fibonacci sequence
132486
Induction proof on Fibonacci sequence: $F(n-1) \cdot F(n+1) - F(n)^2 = (-1)^n$
138267
What is the sum of Fibonacci reciprocals?
116518
Proof by induction: $n$th Fibonacci number is at most $ 2^n$
146826
Fibonacci Sequence and series limits
45392
Every natural number can be written as the sum of distinct Fibonacci numbers?
67886
How to prove $\sum_{k=1}^{n}F_k = F_{n+2}-1$ by induction when $F_n$ is the Fibonacci sequence
49741
Finding a closed form for a recurrence relation $a_n=3a_{n-1}+4a_{n-2}$
42435
Proof of this result related to Fibonacci numbers: $\begin{pmatrix}1&1\\1&0\end{pmatrix}^n=\begin{pmatrix}F_{n+1}&F_n\\F_n&F_{n-1}\end{pmatrix}$?
83421
Checking if a number is a Fibonacci or not?
130820
The generating function for the Fibonacci numbers
131400
Solution check: Let $f_n$ be fibonacci numbers. Prove: $\sum_{k=0}^{n-1} \binom{n+k}{2k+1} = f_{2n-1}$ and $\sum_{k=0}^n \binom{n+k}{2k} = f_{2n}$
925
Prove that $F_n={n-1 \choose 0 }+{n-2 \choose 1 }+{n-3 \choose 2 }+\ldots$ where $F(n)$ is the $n$-th fibonacci number
132089
How do I prove/disprove that $F_n^2 + F_{n\pm 1}^2 = F_{2n\pm 1}$, where $F_n$ is the $n$th Fibonacci number?
100781
Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$
17269
Strong Induction Proof: Fibonacci number even if and only if 3 divides index