MathDB
k(m) is even

Source: 2022 Viet Nam math olympiad for high school students D2 P8

March 22, 2023
algebranumber theory

Problem Statement

Given Fibonacci sequence (Fn),(F_n), and a positive integer mm, denote k(m)k(m) by the smallest positive integer satisfying Fn+k(m)≡Fn( mod m),F_{n+k(m)}\equiv F_n(\bmod m), for all natural numbers nn.
Prove that: k(m)k(m) is even for all m>2.m>2.
Back to ProblemsView on AoPS