On a Romanoff type problem of Erdős and Kalmár

Yuchen Ding

doi:10.48550/arxiv.2503.22700

March 17, 2025Open Access

On a Romanoff type problem of Erdős and Kalmár

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Key Points

The study shows that for almost all integers greater than 1, the lower asymptotic density is positive.
Specifically, it proves that integers of the form p + floor(y^k) exhibit this behavior, where p is prime.
Formulating this in terms of Erdős and Kalmár's problem highlights significant progress in understanding density properties.
This finding may encourage further exploration of prime-related density phenomena in number theory.

Implication

This analysis reveals positive lower asymptotic density in sets of integers involving primes, indicating important properties in number theory.

Abstract

Let N and P be the sets of natural numbers and primes, respectively. Motived by an old problem of Erd os and Kalmár, we prove that for almost all $y>1$ the lower asymptotic density of integers of the form p+ yᵏ~(p∈ P,k∈ N) is positive.

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Cite This Study

Yuchen Ding (2025) studied this question.

synapsesocial.com/papers/68e02f46f0e39f13e7fa2f9c https://doi.org/10.48550/arxiv.2503.22700

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On a Romanoff type problem of Erdős and Kalmár

Key Points

Implication

Abstract

Discussion

Cite This Study

On a Romanoff type problem of Erdős and Kalmár

Key Points

Implication

Abstract

Discussion

Cite This Study

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