F. Luca

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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 $p$ .

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

Numbers of the form k+f(k)

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

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