Proving it is impossible; on Erdős problem $\# 278$

Erdős asked many mathematical questions. Some lead to exciting research, others turned out to be easily solved. In this article, we provide evidence that one of his questions, Erdős problem \#278 , has no general answer. We do so by relating it with a hard knapsack problem instance,and by demonstrating that different, non-equivalent formulas arise depending on the structure of the moduli.

Publication Details

Journal
ArXiv.org
Published
2025-08-25
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

Proving it is impossible; on Erdős problem $\# 278$

ArXiv.org
Geochemistry and Geologic Mapping
article

Proving it is impossible; on Erdős problem $\# 278$

article en

Abstract

Erdős asked many mathematical questions. Some lead to exciting research, others turned out to be easily solved. In this article, we provide evidence that one of his questions, Erdős problem \#278 , has no general answer. We do so by relating it with a hard knapsack problem instance,and by demonstrating that different, non-equivalent formulas arise depending on the structure of the moduli.

ArXiv.org
Openalex Percentile: Top 64%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
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Proving it is impossible; on Erdős problem $\# 278$ · ArXiv.org (2025) | TGRS Research Map | TGRS