Work

Proof of Erdős Problem #369: Consecutive Smooth Integers Near N

Year: 2026

Type: article

Abstract: This Zenodo record contains the manuscript and source files for “Proof of Erdos Problem 369: Consecutive Smooth Integers Near N”. The paper studies strings of consecutive smooth integers near N and proves that for every ε > 0 and every integer k >= 2, every sufficiently large N admits a block of k consecutive N^ε-smooth integers in [N/2, N]. The main tools are cyclotomic factorization, Euler-totient estimates, and a multiplicative covering argument based on powers of 2ᴸ and 3ᴸ.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.19361033

Author: Yang, Yueer

Institution: University of Maryland, College Park

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7147592534

FWCI:

Cites:

Cited by:

Related to: