Exact divisibility properties of some subsequences of fibonacci numbers

• Main Authors: Chatchawan Panraksa, Aram Tangboonduangjit, Keng Wiboonton
• Other Authors: Mahidol University
• Format: Article
• Published: 2018
• Subjects: Mathematics
• Online Access: https://repository.li.mahidol.ac.th/handle/123456789/32013

For each positive integer n, we consider the following sequence of numbers F(n), F(nF(n)), F(nF(nF(n))), ⋯, where F(n) is the nth Fibonacci number defined in the usual way. Let Gk(n) be the kth term of this sequence. We prove that F(n)k || Gk(n) for all positive integers k and n with n > 3. For t...