Výsledky vyhledávání - "Calvo, L. A."

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Markoff $m$-triples with $k$-Fibonacci components

Autor: Alfaya, D., Calvo, L. A., de Guinea, A. Martínez, Rodrigo, J., Srinivasan, A.

We classify all solution triples with $k$-Fibonacci components to the equation $x^2+y^2+z^2=3xyz+m,$ where $m$ is a positive integer and $k\geq 2$. As a result, for $m=8$, we have the Markoff triples with Pell components $(F_2(2), F_2(2n), F_2(2n+2))

Externí odkaz: http://arxiv.org/abs/2409.13885

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Markoff-Fibonacci m-triples

Autor: Alfaya, D., Calvo, L. A., de Guinea, A. Martínez, Rodrigo, J., Srinivasan, A.

We classify all solution triples with Fibonacci components to the equation $a^2+b^2+c^2=3abc+m,$ for positive $m$. We show that for $m=2$ they are precisely $(1,F(b),F(b+2))$, with even $b$; for $m=21$, there exist exactly two Fibonacci solutions $(1

Externí odkaz: http://arxiv.org/abs/2405.08509

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Minimal triples for a generalized Markoff equation

Autor: Srinivasan, A., Calvo, L. A.

For a positive integer $m>1$, if the generalized Markoff equation $a^2+b^2+c^2=3abc+m$ has a solution triple, then it has infinitely many solutions. We show that all positive solution triples are generated by a finite set of triples that we call mini

Externí odkaz: http://arxiv.org/abs/2307.10470

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