Congruences of the q-Fibonacci sequence related with its transcendence

2023/01/07 by Takumi Anzawa, Anzawa, Takumi, Hidetaka Funakura +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2301.02838

openalex publication_date 2023/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using Andrews's explicit formulae of the q-Fibonacci sequence introduced by Schur, we prove certain congruences of the q-Fibonacci sequence which relate the sequence with the original Fibonacci sequence. As a corollary, we show that it yields a transcendental element in the ℚ-algebra \mathscrA of integers modulo infinitely large primes under the generalized Riemann hypothesis.

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