F. Luca

collaborators

3 papers

math.NT2026

On Carmichael numbers of the form $2^{n} p^{m} + 1$

Florian Luca

Here, we show that if $m \geq 5$ is fixed and odd, then there are only finitely many Carmichael numbers of the form $2^{n} p^{m} + 1$ for positive integers $n$ and prime $p$ .

cs.FL2023

Transcendence of Sturmian Numbers over an Algebraic Base

Florian Luca, Joel Ouaknine, James Worrell

We consider numbers of the form $S_{β} (u) := \sum_{n = 0}^{\infty} \frac{u _{n}}{β ^{n}}$ for $u = ⟨ u_{n} ⟩_{n = 0}^{\infty}$ a Sturmian sequence over a binary alp…

math.NT2023

Numbers of the form $k + f (k)$

Mikhail R. Gabdullin, Vitalii V. Iudelevich, Florian Luca

For a function $f : N \to N$ , let $$ N^+_f(x)=\{n\leq x: n=k+f(k) \mbox{ for some } k\}. $$ Let $τ (n) = \sum_{d ∣ n} 1$ be the divisor function, $ω (n) = \sum_{p ∣ n} 1$ b…

On Carmichael numbers of the form 2npm+1

Transcendence of Sturmian Numbers over an Algebraic Base

Numbers of the form k+f(k)

On Carmichael numbers of the form $2^{n} p^{m} + 1$

Numbers of the form $k + f (k)$