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Diophantine quadruples with values in $k$-generalized Fibonacci numbers

In: Mathematica Slovaca, vol. 68, no. 4
Carlos Alexis Gómez Ruiz - Florian Luca
Detaily:
Rok, strany: 2018, 939 - 949
Kľúčové slová:
generalized Fibonacci numbers, Diophantine quadruples
O článku:
We consider for integers $k≥ 2$ the $k$–generalized Fibonacci sequences $F(k):=$ \linebreak $(Fn(k))n≥ 2-k$, 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 $aiaj + 1$ ($i\neq j$) are all members of $F(k)$.
Ako citovať:
ISO 690:
Ruiz, C., Luca, F. 2018. Diophantine quadruples with values in $k$-generalized Fibonacci numbers. In Mathematica Slovaca, vol. 68, no.4, pp. 939-949. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0156

APA:
Ruiz, C., Luca, F. (2018). Diophantine quadruples with values in $k$-generalized Fibonacci numbers. Mathematica Slovaca, 68(4), 939-949. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0156
O vydaní:
Publikované: 10. 8. 2018