Geodesic
Fermat $k$-Fibonacci and $k$-Lucas numbers
Mathematica Bohemica, Tome 145 (2020) no. 1, pp. 19-32.

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Using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and Pethő, we find all $k$-Fibonacci and $k$-Lucas numbers which are Fermat numbers. Some more general results are given.
DOI : 10.21136/MB.2018.0015-18
Classification : 11B39, 11J86
Keywords: generalized Fibonacci number; Fermat number, linear form in logarithms; reduction method 
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Bravo, Jhon J.; Herrera, Jose L. Fermat $k$-Fibonacci and $k$-Lucas numbers. Mathematica Bohemica, Tome 145 (2020) no. 1, pp. 19-32. doi : 10.21136/MB.2018.0015-18. http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0015-18/

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