On a conjecture of Erdős

2022/01/25 by Yong-Gao Chen, Chen, Yong-Gao, Yuchen Ding +1
Mathematics · #11A41 #11A67 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.10727

openalex publication_date 2022/01/26 · openalex created_date 2022/07/19 · openalex updated_date 2026/07/28

Abstract

Let P denote the set of all primes. In 1950, P. Erdős conjectured that if c is an arbitrarily given constant, x is sufficiently large and a₁,… , a_t are positive integers with a₁log x, then there exists an integer n so that the number of solutions of n=p+a_i (p∈ P, 1≤ i≤ t) is greater than c. In this note, we confirm this old conjecture of Erdős.

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