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A ternary additive problem involving fractional powers

Raymond Luo and Gang Yu

Vol. 15 (2022), No. 4, 629–640
Abstract

We identify real numbers c > 1, as large as possible, such that every large integer N can be expressed as

N = [uc] + [vc] + [wc],

where u,v,w are positive integers. We also consider the cases with one or two of u,v,w from a sparse subset of positive integers.

Keywords
fractional powers, Diophantine equation, exponential sum
Mathematical Subject Classification
Primary: 11D85
Secondary: 11L07
Milestones
Received: 1 February 2021
Revised: 10 January 2022
Accepted: 19 January 2022
Published: 7 January 2023

Communicated by Kenneth S. Berenhaut
Authors
Raymond Luo
Montgomery Blair High School
Silver Spring, MD
United States
Carnegie Mellon University
Pittsburgh, PA
United States
Gang Yu
Department of Mathematical Sciences
Kent State University
Kent, OH
United States