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<p>Two positive integers belong to the same power of two-class if they share the same odd part. In this paper, we use lower bounds for linear forms in logarithms, reduction techniques in Diophantine approximation, and the LLL algorithm to find all generalized Fibonacci and Pell numbers belonging to the same power of two-class. To achieve this, we solve two Diophantine equations involving terms of these sequences, which are interesting in their own right. This paper continues and extends the previous work of Gómez and Luca [<CitationRef CitationID="CR15">15</CitationRef>].</p>

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Powers of two-classes in generalized Fibonacci and Pell sequences

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • Jhon J. Bravo,
  • Jose L. Herrera,
  • Julieth F. Ruiz

摘要

Two positive integers belong to the same power of two-class if they share the same odd part. In this paper, we use lower bounds for linear forms in logarithms, reduction techniques in Diophantine approximation, and the LLL algorithm to find all generalized Fibonacci and Pell numbers belonging to the same power of two-class. To achieve this, we solve two Diophantine equations involving terms of these sequences, which are interesting in their own right. This paper continues and extends the previous work of Gómez and Luca [15].