Pell numbers close to Fibonacci numbers

In this paper, we determine all members of the Pell sequence which are close to Fibonacci numbers using a concept of closeness given by Chern and Cui (Fibonacci Quart 52:344–348, 2014). That is, we find all the solutions of the Diophantine inequality \(|P_n - F_m| < F_{m}^{1/2}\) $|P_n-F_m|<F_m^{1/2}$ in positive integers n and m. This paper continues the previous work (Chern and Cui, Fibonacci Quart 52:344–348, 2014) that found all Fibonacci numbers close to a power of 2.