Fermat $k$-Fibonacci and $k$-Lucas numbers

Abstract

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.

Keywords

• generalized fibonacci number
• fermat number, linear form in logarithms
• reduction method