On arithmetic progressions of positive integers avoiding p+F_m and q+L_n

2025/05/26 by Wang, Rui-Jing
#11B39 #11P32 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.2506.12047

Abstract

In this paper, it is proved that there is an arithmetic progression of positive integers such that each of which is expressible neither as p+F_m nor as q+L_n, where p,q are primes, F_m denotes the m -th Fibonacci number and L_n denotes the n -th Lucas number.

Citations

• A counterexample of two Romanov type conjectures
• Quantitative results of the Romanov type representation functions
• On the integers not of the form p+2^a+2^b

Related

• On arithmetic progressions in Lucas sequences
• Narrow arithmetic progressions in the primes
• Arithmetic progressions consisting of unlike powers
• Progressions arithmétiques dans les nombres premiers, d'après B. Green et T. Tao
• Integers without divisors from a fixed arithmetic progression