Carlo Sanna

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20242026

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math.NT2026

Another factor of integer polynomials with minimal integrals

Alice Bazzanella, Carlo Sanna

Let $N$ be a positive integer and let $S_{N}$ be the set of polynomials with integer coefficients, degree less than $N$ , and minimal positive integral over $[0, 1]$ . D. Bazzanella ini…

math.NT2026

Explicit inequalities for the nth lucky number

Carlo Sanna

Gardiner, Lazarus, Metropolis, and Ulam introduced a variation of the sieve of Eratosthenes that (instead of producing the sequence of prime numbers) produces the sequence of "luck…

math.NT2025

A lower bound for the number of Egyptian fractions

Sandro Bettin, Loïc Grenié, Giuseppe Molteni +1

An Egyptian fraction is a sum of the form $1/ n_{1} + \dots + 1/ n_{r}$ where $n_{1}, \dots, n_{k}$ are distinct positive integers. We prove explicit lower bounds for the cardinality of the…

math.NT2024

Counting numbers that are divisible by the product of their digits

Qizheng He, Carlo Sanna

Let $b \geq 3$ be a positive integer. A natural number is said to be a base- $b$ Zuckerman number if it is divisible by the product of its base- $b$ digits. Let $Z_{b} (x)$ be…

math.NT2024

On the number of residues of certain second-order linear recurrences

Federico Accossato, Carlo Sanna

For every monic polynomial $f \in Z [X]$ with $deg (f) \geq 1$ , let $L (f)$ be the set of all linear recurrences with values in $Z$ and char…