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Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$

Proving that $f_2+f_4+\cdots+f_{2n}=f_{2n+1}-1$ for Fibonacci numbers by induction

Use of the Reciprocal Fibonacci constant?

Primality test for Proth numbers using Fibonacci numbers

Fibonacci numbers, sum of squares and divisibility

Fibonacci, compositions, history

Prove that for the Fibonacci sequence $(F_n)$, $F_n$ divides $F_{2n}$.

Fibonacci numbers and proof by induction

Another Fibonacci identity: $F_{2n-1} = F_{n}^2 + F_{n-1}^2$

Fiboncacci theorem: Proof by induction that $F_{n} \cdot F_{n+1} - F_{n-2}\cdot F_{n-1}=F_{2n-1}$

How can I show that $\sum\limits_{n=1}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}$ is algebraic?

Dominos ($2 \times 1$ on $2 \times n$ and on $3 \times 2n$)

Why the $GCD$ of any two consecutive Fibonacci numbers is $1$?

Proof by induction on Fibonacci numbers: show that $f_n\mid f_{2n}$

New posts in fibonacci-numbers

Recurrences for even and odd indexed of Fibonacci Numbers

Log Fibonacci Equals to Theta

What is the name of the "unique" numbers in Fibonacci-like integer sequences?

Show that log $Fib_{n}$ is $\theta(n)$

Fibonacci numbers divisible by $9$

Is $n^7 - 77$ ever a Fibonacci number?

Prove the $n$th Fibonacci number is the integer closest to $\frac{1}{\sqrt{5}}\left( \frac{1 + \sqrt{5}}{2} \right)^n$

Proving that $f_2+f_4+\cdots+f_{2n}=f_{2n+1}-1$ for Fibonacci numbers by induction

Use of the Reciprocal Fibonacci constant?

Primality test for Proth numbers using Fibonacci numbers

Fibonacci numbers, sum of squares and divisibility

Fibonacci, compositions, history

Prove that for the Fibonacci sequence $(F_n)$, $F_n$ divides $F_{2n}$.

Fibonacci numbers and proof by induction

Another Fibonacci identity: $F_{2n-1} = F_{n}^2 + F_{n-1}^2$

Fiboncacci theorem: Proof by induction that $F_{n} \cdot F_{n+1} - F_{n-2}\cdot F_{n-1}=F_{2n-1}$

How can I show that $\sum\limits_{n=1}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}$ is algebraic?

Dominos ($2 \times 1$ on $2 \times n$ and on $3 \times 2n$)

Why the $GCD$ of any two consecutive Fibonacci numbers is $1$?

Proof by induction on Fibonacci numbers: show that $f_n\mid f_{2n}$