2 papers
math.NT2025
Diophantine equations over the generalized Fibonacci sequences: exploring sums of powers
Roberto Alvarenga, Ana Paula Chaves, Maria Eduarda Ramos +2
Let (F_n)_{n} be the classical Fibonacci sequence. It is well-known that it satisfies F_{n}^2 + F_{n+1}^2 = F_{2n+1}. In this study, we explore generalizations of this Diophantine…
math.NT2025
Fibonacci Numbers as Sums of Consecutive Terms in -Generalized Fibonacci Sequence
Roberto Alvarenga, Ana Paula Chaves, Maria Eduarda Ramos +2
Let (F_n^{(k)})_{n\geq -(k-2)} be the k-generalized Fibonacci sequence, defined as the linear recurrence sequence whose first k terms are \(0, 0, \ldots, 0, 1\), and whose subseque…