Patrick Letendre

collaborators

3 papers

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 $1 = d_{1} < d_{2} < \dots < d_{I ¨ (n)} = n$ 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 $I ¨ (n)$ divisors of $n$ . We study the function $D_{n} (X, Y) := ∣ {d \in D_{n} : X \leq d \leq X + Y} ∣$ for $Y…

The abc Conjecture Revisited

The Vandermonde Determinant of the Divisors of an Integer

Divisors of an Integer in a Short Interval

The $ab c$ Conjecture Revisited