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Abstract We consider for integers k ≥ 2 the k–generalized Fibonacci sequences F(k) := (Fn(k))n≥2−k, $\begin{array}{} (F_n^{(k)})_{n\geq 2-k}, \end{array} $ whose first k terms are 0, …, 0, 1 and… Click to show full abstract
Abstract We consider for integers k ≥ 2 the k–generalized Fibonacci sequences F(k) := (Fn(k))n≥2−k, $\begin{array}{} (F_n^{(k)})_{n\geq 2-k}, \end{array} $ whose first k terms are 0, …, 0, 1 and each term afterwards is the sum of the preceding k terms. In this paper, we show that there does not exist a quadruple of positive integers a1 < a2 < a3 < a4 such that aiaj + 1 (i ≠ j) are all members of F(k).
Keywords:
quadruples values;
fibonacci numbers;
generalized fibonacci;
diophantine quadruples;
values generalized
Journal Title: Mathematica Slovaca
Year Published: 2018
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Journal Title: Mathematica Slovaca
Year Published: 2018
Link to full text (if available)
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recommendations!