On Arithmetic Progressions of Positive Integers Avoiding p + F_m and q + L_n

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.

Keywords

Fibonacci number / Lucas number / arithmetic progression / covering system / prime / 11P32 / 11B39

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Peking University