# Questions tagged [fibonacci-numbers]

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### Avoiding the Fibonacci numbers

For given positive integers $a$ and $b$, let $(a,b)$ be "special" if $an+b$ is not a Fibonacci number for every positive integer $n$. For instance, $(8,4)$ and $(8,6)$ are special. There are ...
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### Conjecture about primes and Fibonacci numbers

I posted this conjecture on math.stackexchange, but I received no answer proving or disproving it: if $m > 4$ is a positive integer not divisible by $2$ or $3$, it's ever possible to find a ...
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### The Fibonacci sequence modulo $5^n$

Let $(F_k)_{k=0}^\infty$ be the classical Fibonacci sequence, defined by the recursive formula $F_{k+1}=F_k+F_{k-1}$ where $F_0=0$ and $F_1=1$. For every $n\in\mathbb N$ let $\pi(n)$ be the smallest ...
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### Reciprocals of Fibonacci numbers

Is the sum of the reciprocals of Fibonacci numbers a transcendental?