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Let {F n}n≥0 be the sequence of Fibonacci numbers. The aim of this paper is to give linear independence results over (5) for the infinite series n=1χj(n)/Fn with certain nonprincipal real Dirichlet characters χ j. We also deduce the irrationality results for the special principal Dirichlet characters and for other multiplicative functions.

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For any positive integer n let Fn be the n-th Fibonacci number. Given positive integers a and b, we study the size of the greatest common divisor of Fn + a and Fm + b for varying positive integers m and n.

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partition of generalized Fibonacci number, Sankhya , Series A , 29 ( 1996 ), 207 – 214 . [11] Mohanty , S. G. , Lattice Path Counting and Applications , New York

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