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.
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

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