科研之友
微信
新浪微博
Facebook
分享链接
摘要
For k >= 2, the k-generalized Fibonacci sequence (F-n((k)))(n) is defined by the initial values 0, 0, . . . , 0, 1 (k terms) and such that each term afterwards is the sum of the k preceding terms. In this paper, we shall prove that the only solutions of the Diophantine equation
F-n((k)) = k2(m) + 1
in positive integers m, n and k >= 2, are (n, k, m) = (5, 2, 1), (5, 3, 1) and (6,3, 2). For that, we shall use lower bounds for linear forms in logarithms together with a computational approach using Mathematica software.
- 出版日期2016-11
