C. Sanna

activity

20122023

most citedOn the p-adic denseness of the quotient set of a polynomial image

12 citations · 106 across the 43 of their papers we have counts for

collaborators

51 papers

math.NT2023

A note on the power sums of the number of Fibonacci partitions

Carlo Sanna

For every nonnegative integer $n$ , let $r_{F} (n)$ be the number of ways to write $n$ as a sum of Fibonacci numbers, where the order of the summands does not matter. Moreover, for all…

math.CO2023

On the distribution of the entries of a fixed-rank random matrix over a finite field

Carlo Sanna

Let $r > 0$ be an integer, let $F_{q}$ be a finite field of $q$ elements, and let $A$ be a nonempty proper subset of $F_{q}$ . Moreover, let $M$ be…

math.NT2023

On the inverse of a Fibonacci number modulo a Fibonacci number being a Fibonacci number

Carlo Sanna

Let $(F_{n})_{n \geq 1}$ be the sequence of Fibonacci numbers. For all integers $a$ and $b \geq 1$ with $g cd (a, b) = 1$ , let $[a^{- 1} mod b]$ be the multiplicative inverse of $a…

cs.CR2023★ 1 cited

Smaller public keys for MinRank-based schemes

Antonio J. Di Scala, Carlo Sanna

MinRank is an NP-complete problem in linear algebra whose characteristics make it attractive to build post-quantum cryptographic primitives. Several MinRank-based digital signature…

math.NT2022

On the index of appearance of a Lucas sequence

Carlo Sanna

Let $u = (u_{n})_{n \geq 0}$ be a Lucas sequence, that is, a sequence of integers satisfying $u_{0} = 0$ , $u_{1} = 1$ , and $u_{n} = a_{1} u_{n - 1} + a_{2} u_{n - 2}$ for every intege…

math.NT2022

On the greatest common divisor of $n$ and the $n$ th Fibonacci number, II

Abhishek Jha, Carlo Sanna

Let $A$ be the set of all integers of the form $g cd (n, F_{n})$ , where $n$ is a positive integer and $F_{n}$ denotes the $n$ th Fibonacci number. Leonetti and Sanna proved tha…

math.NT2022★ 1 cited

Greatest common divisors of shifted primes and Fibonacci numbers

Abhishek Jha, Carlo Sanna

Let $(F_{n})$ be the sequence of Fibonacci numbers and, for each positive integer $k$ , let $P_{k}$ be the set of primes $p$ such that $g cd (p - 1, F_{p - 1}) = k$ . We prove t…

math.NT2022

Zeckendorf representation of multiplicative inverses modulo a Fibonacci number

Gessica Alecci, Nadir Murru, Carlo Sanna

Prempreesuk, Noppakaew, and Pongsriiam determined the Zeckendorf representation of the multiplicative inverse of $2$ modulo $F_{n}$ , for every positive integer $n$ not divisible by $…

math.NT2022

RLWE and PLWE over cyclotomic fields are not equivalent

Antonio J. Di Scala, Carlo Sanna, Edoardo Signorini

We prove that the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems over the cyclotomic field $Q (ζ_{n})$ are not equivalent. Precisely…

math.NT2021

A Survey on Coefficients of Cyclotomic Polynomials

Carlo Sanna

Cyclotomic polynomials play an important role in several areas of mathematics and their study has a very long history, which goes back at least to Gauss (1801). In particular, the…

math.NT2021

On the number of residues of linear recurrences

Carlo Sanna

For every nonconstant monic polynomial $g \in Z [X]$ , let $M (g)$ be the set of positive integers $m$ for which there exist an integer linear recurrence $(s_n)_{n…

math.NT2021

On the l.c.m. of shifted Lucas numbers

Carlo Sanna

Let $(L_{n})_{n \geq 1}$ be the sequence of Lucas numbers, defined recursively by $L_{1} := 1$ , $L_{2} := 3$ , and $L_{n + 2} := L_{n + 1} + L_{n}$ , for every integer $n \geq 1$ . We determi…

math.NT2021

Membership in random ratio sets

Carlo Sanna

Let $A$ be a random set constructed by picking independently each element of ${1, \dots, n}$ with probability $α \in (0, 1)$ . We give a formula for the probability that…

math.NT2021★ 1 cited

On the least common multiple of shifted powers

Carlo Sanna

Let $a \geq 2$ be an integer. We prove that for every periodic sequence $(s_{n})_{n \geq 1}$ in ${- 1, + 1}$ there exists an effectively computable rational number $C_{s} > 0$ …

math.NT2021★ 2 cited

Additive bases and Niven numbers

Carlo Sanna

Let $g \geq 2$ be an integer. A natural number is said to be a base- $g$ Niven number if it is divisible by the sum of its base- $g$ digits. Assuming Hooley's Riemann Hypothesis, we…

math.NT2020

On the least common multiple of random $q$ -integers

Carlo Sanna

For every positive integer $n$ and for every $α \in [0, 1]$ , let $B (n, α)$ denote the probabilistic model in which a random set $A \subseteq {1, \dots, n}$ is…

math.NT2020

On the divisibility of the rank of appearance of a Lucas sequence

Carlo Sanna

Let $U = (U_{n})_{n \geq 0}$ be a Lucas sequence and, for every prime number $p$ , let $ρ_{U} (p)$ be the rank of appearance of $p$ in $U$ , that is, the smallest positive integer $k$ suc…

math.RA2020

The Largest Entry in the Inverse of a Vandermonde Matrix

Carlo Sanna, Jeffrey Shallit, Shun Zhang

We investigate the size of the largest entry (in absolute value) in the inverse of certain Vandermonde matrices. More precisely, for every real $b > 1$ , let $M_{b} (n)$ be the maximum…

math.NT2020

On the l.c.m. of shifted Fibonacci numbers

Carlo Sanna

Let $(F_{n})_{n \geq 1}$ be the sequence of Fibonacci numbers. Guy and Matiyasevich proved that \begin{equation*} \log \operatorname{lcm} (F_1, F_2, \dots, F_n) \sim \frac{3 \log α}{…

math.NT2020★ 3 cited

A note on the natural density of product sets

Sandro Bettin, Dimitris Koukoulopoulos, Carlo Sanna

Given two sets of natural numbers $A$ and $B$ of natural density $1$ we prove that their product set $\mathcal{A}\cdot \mathcal{B}:=\{ab:a\in\mathcal{A},\,b\in\…

math.NT2020

Practical central binomial coefficients

Carlo Sanna

A practical number is a positive integer $n$ such that all positive integers less than $n$ can be written as a sum of distinct divisors of $n$ . Leonetti and Sanna proved that, as $…

math.NT2020★ 9 cited

On the condition number of the Vandermonde matrix of the nth cyclotomic polynomial

Antonio J. Di Scala, Carlo Sanna, Edoardo Signorini

Recently, Blanco-Chacón proved the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for some families of cyclotomic number fields by g…

math.NT2020★ 2 cited

Lucas pseudoprimes and the Pell conic

Antonio J. Di Scala, Nadir Murru, Carlo Sanna

We show a connection between the Lucas pseudoprimes and the Pell conic equipped with the Brahmagupta product introducing the Pell pseudoprimes.

math.NT2019★ 6 cited

A note on product sets of random sets

Carlo Sanna

Given two sets of positive integers $A$ and $B$ , let $A B := {ab : a \in A, b \in B}$ be their product set and put $A^{k} := A \dots A$ ( $k$ times $A$ ) for any positive integer $…

A note on the power sums of the number of Fibonacci partitions

On the distribution of the entries of a fixed-rank random matrix over a finite field

On the inverse of a Fibonacci number modulo a Fibonacci number being a Fibonacci number

Smaller public keys for MinRank-based schemes

On the index of appearance of a Lucas sequence

On the greatest common divisor of n and the nth Fibonacci number, II

Greatest common divisors of shifted primes and Fibonacci numbers

Zeckendorf representation of multiplicative inverses modulo a Fibonacci number

RLWE and PLWE over cyclotomic fields are not equivalent

A Survey on Coefficients of Cyclotomic Polynomials

On the number of residues of linear recurrences

On the l.c.m. of shifted Lucas numbers

Membership in random ratio sets

On the least common multiple of shifted powers

Additive bases and Niven numbers

On the least common multiple of random q-integers

On the divisibility of the rank of appearance of a Lucas sequence

The Largest Entry in the Inverse of a Vandermonde Matrix

On the l.c.m. of shifted Fibonacci numbers

A note on the natural density of product sets

Practical central binomial coefficients

On the condition number of the Vandermonde matrix of the nth cyclotomic polynomial

Lucas pseudoprimes and the Pell conic

A note on product sets of random sets

On the greatest common divisor of $n$ and the $n$ th Fibonacci number, II

On the least common multiple of random $q$ -integers