MathDB
Prove this expression on fibonacci numbers is divisible by 150 for any n

Source: 2019 Jozsef Wildt International Math Competition

May 19, 2020
Fibonacci sequencenumber theory

Problem Statement

Let fnf_n be nnth Fibonacci number defined by recurrence fn+1−fn−fn−1=0f_{n+1} - f_n - f_{n-1} = 0, n∈Nn \in \mathbb{N} and initial conditions f0=0f_0 = 0, f1=1f_1 = 1. Prove that for any n∈Nn \in \mathbb{N} (n−1)(n+1)(2nfn+1−(n+6)fn)(n - 1) (n + 1) (2nf_{n+1} - (n + 6) f_n)is divisible by 150 for any n∈Nn \in \mathbb{N}.
Back to ProblemsView on AoPS