Resolution of an Erdős' problem on least common multiples

2024/10/11 by Stijn Cambie, Cambie, Stijn
Mathematics · #11A05 #11A07 #11A51 #Algebraic and Geometric Analysis #Differential Equations and Boundary Problems #FOS: Mathematics #General Mathematics (math.GM) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2410.09138

openalex publication_date 2024/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Erdős posed the question whether there exist infinitely many sets of consecutive numbers whose least common multiple (lcm) exceeds the lcm of another, larger set with greater consecutive numbers. In this paper, we answer this question affirmatively by proving that the ratio of the lcm's can be made arbitrarily large.

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