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<p>This paper is the continuation of Hajdu and Tijdeman (Ramanujan J 66:Article 74, 2025), where we deal with Lucas sequences. Here we study integers represented by integer sequences which satisfy binary recursive relations. In the case of non-degenerate sequences we give an upper bound on the largest index of a zero term and bounds on the growth order of the absolute values of the terms, both only in terms of the two initial values, which is a novel feature. Some of these bounds are best possible apart from a multiplicative constant.</p>

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Integers represented by binary recursive sequences

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月8日

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  • Lajos Hajdu,
  • Rob Tijdeman

摘要

This paper is the continuation of Hajdu and Tijdeman (Ramanujan J 66:Article 74, 2025), where we deal with Lucas sequences. Here we study integers represented by integer sequences which satisfy binary recursive relations. In the case of non-degenerate sequences we give an upper bound on the largest index of a zero term and bounds on the growth order of the absolute values of the terms, both only in terms of the two initial values, which is a novel feature. Some of these bounds are best possible apart from a multiplicative constant.