2024/08/13 by Deepa Antony, Antony, Deepa, Rupam Barman +1
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2408.06949
openalex publication_date 2024/08/13 · openalex created_date 2024/09/11 · openalex updated_date 2026/07/28
Let (xn)n≥0 be a linear recurrence sequence of order k≥2 satisfying xn=a1xn-1+a2xn-2+…+akxn-k for all integers n≥ k, where a1,…,ak,x0,…, xk-1∈ ℤ, with ak≠0. In 2017, Sanna posed an open question to classify primes p for which the quotient set of (xn)n≥0 is dense in ℚp. In a recent paper, we showed that if the characteristic polynomial of the recurrence sequence has a root ± α, where α is a Pisot number and if p is a prime such that the characteristic polynomial of the recurrence sequence is irreducible in ℚp, then the quotient set of (xn)n≥ 0 is dense in ℚp. In this article, we answer the problem for certain linear recurrence sequences whose characteristic polynomials are reducible over ℚ.