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Keywords:
generalized Fibonacci number; Fermat number, linear form in logarithms; reduction method
generalized Fibonacci number; Fermat number, linear form in logarithms; reduction method
Summary:
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.
References:
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