On additive and multiplicative decompositions of sets of integers with restricted prime factors, I. (Smooth numbers.)

2020/06/27 by Kálmán Győry, Lajos Hajdu, Győry, K. +3
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2006.15307

Abstract

In [10] the third author of this paper presented two conjectures on the additive decomposability of the sequence of ''smooth'' (or ''friable'') numbers. Elsholtz and Harper [4] proved (by using sieve methods) the second (less demanding) conjecture. The goal of this paper is to extend and sharpen their result in three directions by using a different approach (based on the theory of S-unit equations).

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