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

K. Győry; L. Hajdu; A. Sárközy

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arXiv · 2006.15307

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

K. Győry·L. Hajdu·A. Sárközy

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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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BibTeX RIS

K. Győry, L. Hajdu, A. Sárközy. 2020-06-27. On additive and multiplicative decompositions of sets of integers with restricted prime factors, I. (Smooth numbers.). https://arxiv.org/abs/2006.15307

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