New posts in fibonacci-numbers

Why does a golden angle based spiral produce evenly distributed points?

fibonacci-numbers golden-ratio equidistribution

If the generating function summation and zeta regularized sum of a divergent series exist, do they always coincide?

analysis fibonacci-numbers divergent-series

Prove that $\forall p \in \Bbb P;p \ne 5,$ $F_{p^n - \left(\frac{5}{p}\right)p^{n-1}} \equiv 0 \mod p^n$

prime-numbers modular-arithmetic fibonacci-numbers

A number $N$ is a $k$-nacci number if and only if ...

number-theory fibonacci-numbers

why $\frac{f_n}{f_kf_{n-k}}$ is an integer for this sequence

sequences-and-series number-theory fibonacci-numbers algebraic-combinatorics

For which complex numbers $\alpha$ and $\beta$ is it true that $\alpha^n+\beta^n$ is always an integer?

elementary-number-theory algebraic-geometry fibonacci-numbers

Experimental identities with Fibonacci series

real-analysis sequences-and-series number-theory summation fibonacci-numbers

Showing the Fibonacci inequality $f_1^{f_1}f_2^{f_2}f_3^{f_3}\cdots f_n^{f_n}\leq f_1!f_2!f_3!\cdots f_n!\;e^{({f_{n+2}-n-1)}}$ without induction.

calculus sequences-and-series inequality fibonacci-numbers

Infinite sum of reciprocal shifted Fibonacci numbers

sequences-and-series convergence-divergence fibonacci-numbers

Linear Combinations of Fibonacci Numbers (integer coefficients)

elementary-number-theory recreational-mathematics fibonacci-numbers

Do the Fibonacci numbers contain any run of digits?

sequences-and-series elementary-number-theory fibonacci-numbers

Musical and combinatorial proof

combinatorics fibonacci-numbers music-theory

Recurrence and Fibonacci: $a_{n+1}=\frac {1+a_n}{2+a_n}$

recurrence-relations fibonacci-numbers

Closed form for the sum of even fibonacci numbers?

summation fibonacci-numbers closed-form project-euler

Alternative "Fibonacci" sequences and ratio convergence

sequences-and-series fibonacci-numbers

Golden ratio, $n$-bonacci numbers, and radicals of the form $\sqrt[n]{\frac{1}{n-1}+\sqrt[n]{\frac{1}{n-1}+\sqrt[n]{\frac{1}{n-1}+\cdots}}}$

sequences-and-series number-theory limits fibonacci-numbers radicals

Prove or disprove that ${F_{n}}^2 + 41$ is always a composite (if $F_{n}$ is $n^{th}$ Fibonacci number)

elementary-number-theory prime-numbers examples-counterexamples fibonacci-numbers

Fibonacci Cubes: $F_n^3 + F_{n+1}^3 - F_{n-1}^3 =F_{3n}$

elementary-number-theory induction contest-math fibonacci-numbers

Prove $\phi^n = \phi F_n + \text{(another Fibonacci number)}$ using mathematical induction.

induction fibonacci-numbers golden-ratio

Prove that for all $n\geqslant 1$ we have $F_n<{\left(\frac 74\right)}^n$. [closed]

discrete-mathematics inequality fibonacci-numbers