Markov triples with two Fibonacci components
Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 213-243.
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In this paper, we prove that there are at most finitely many pairs of Fibonacci numbers (x,y)=(F m ,F n ) with the property that m≤n and the pair (m,n)∉{(1,2r-1),(1,2),(2,2r+1),(2r+1,2r+3):r≥1} such that (x,y,z) is a Markov triple for some integer z.

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DOI : 10.4171/rsmup/99
Classification : 11 
@article{RSMUP_2022__148__213_0,
     author = {Luca, Florian},
     title = {Markov triples with two {Fibonacci} components},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {213--243},
     volume = {148},
     year = {2022},
     doi = {10.4171/rsmup/99},
     mrnumber = {4542379},
     zbl = {07673828},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/99/}
}
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Luca, Florian. Markov triples with two Fibonacci components. Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 213-243. doi : 10.4171/rsmup/99. http://www.numdam.org/articles/10.4171/rsmup/99/

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