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

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On Arithmetic Progressions of Positive Integers Avoiding p + Fm and q + Ln

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Ruijing Wang

摘要

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 + Fm nor as q + Ln, where p, q are primes, Fm denotes the m-th Fibonacci number and Ln denotes the n-th Lucas number.