12 citations · 106 across the 43 of their papers we have counts for
8 papers · 1 filter
On the least common multiple of random -integers
Carlo Sanna
For every positive integer and for every , let denote the probabilistic model in which a random set is…
On the divisibility of the rank of appearance of a Lucas sequence
Carlo Sanna
Let be a Lucas sequence and, for every prime number , let be the rank of appearance of in , that is, the smallest positive integer suc…
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 , let be the maximum…
On the l.c.m. of shifted Fibonacci numbers
Carlo Sanna
Let 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}{…
A note on the natural density of product sets
Sandro Bettin, Dimitris Koukoulopoulos, Carlo Sanna
Given two sets of natural numbers and of natural density we prove that their product set $\mathcal{A}\cdot \mathcal{B}:=\{ab:a\in\mathcal{A},\,b\in\…
Practical central binomial coefficients
Carlo Sanna
A practical number is a positive integer such that all positive integers less than can be written as a sum of distinct divisors of . Leonetti and Sanna proved that, as $…
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…
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.