Loïc Grenié

collaborators

2 papers

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.NT2019

Counting Egyptian fractions

Sandro Bettin, Loïc Grenié, Giuseppe Molteni +1

For any integer $N \geq 1$ , let $E_{N}$ be the set of all Egyptian fractions employing denominators less than or equal to $N$ . We give upper and lower bounds for the cardi…