Patrick Letendre

collaborators

4 papers

math.NT2026

The Integer Values of $\sum_{i = 1}^{n} \frac{1}{g c d ( n , i )}$

Jean-Marie De Koninck, Patrick Letendre

We study the set of integers $n \leq x$ for which $\sum_{i = 1}^{n} \frac{1}{g c d ( n , i )}$ takes an integer value. We show that the number of such integers is $≪ x^{2/3 + ε}$ for all fix…

math.NT2026

The $ab c$ Conjecture Revisited

Patrick Letendre

We propose a new abc-type conjecture. We motivate the conjecture and illustrate its relevance through several applications. Our main result concerns the function $$ W(x,y) := \sum_…

math.NT2025

The Vandermonde Determinant of the Divisors of an Integer

Patrick Letendre

Let $1 = d_{1} < d_{2} < \dots < d_{τ (n)} = n$ denote the ordered sequence of the positive divisors of an integer $n$ . We are interested in estimating the arithmetic function $$ V(n) :=…

math.NT2025

Divisors of an Integer in a Short Interval

Patrick Letendre

Let $D_{n} \subset N$ denote the set of the $τ (n)$ divisors of $n$ . We study the function $D_{n} (X, Y) := ∣ {d \in D_{n} : X \leq d \leq X + Y} ∣$ for $Y…

The Integer Values of ∑i=1n​gcd(n,i)1​

The abc Conjecture Revisited

The Vandermonde Determinant of the Divisors of an Integer

Divisors of an Integer in a Short Interval

The Integer Values of $\sum_{i = 1}^{n} \frac{1}{g c d ( n , i )}$

The $ab c$ Conjecture Revisited