Garcia, Stephan Ramon; Hong, Yu Xuan; Luca, Florian; Pinsker, Elena; Sanna, Carlo; Schechter, Evan; Starr, Adam \(p\)-adic quotient sets. (English) Zbl 1428.11023 Acta Arith. 179, No. 2, 163-184 (2017). Summary: For \(A \subseteq \mathbb{N}\), the question of when \(R(A) = \{a/a' : a, a' \in A\}\) is dense in the positive real numbers \(\mathbb{R}_+\) has been examined by many authors over the years. In contrast, the \(p\)-adic setting is largely unexplored. We investigate conditions under which \(R(A)\) is dense in the \(p\)-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed. We also pose many open questions that should be of general interest. Cited in 2 ReviewsCited in 12 Documents MSC: 11B05 Density, gaps, topology 11A07 Congruences; primitive roots; residue systems 11B39 Fibonacci and Lucas numbers and polynomials and generalizations Keywords:quotient set; p-adic numbers; density; Fibonacci numbers; sum of powers; geometric progressions PDFBibTeX XMLCite \textit{S. R. Garcia} et al., Acta Arith. 179, No. 2, 163--184 (2017; Zbl 1428.11023) Full Text: DOI arXiv Online Encyclopedia of Integer Sequences: a(n) = 5^(n-1)*(3^n - 1)/2.