MathDB
Fibonacci numbers F_n is divisible by p^m

Source: 2004 VMEO I p2 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__vietnam_mathematical

September 26, 2021
Fibonacci NumbersFibonacci sequenceFibonaccinumber theoryPerfect powerdivisibe

Problem Statement

The Fibonacci numbers (Fn)n=1∞(F_n)_{n=1}^{\infty} are defined as follows: F1=F2=1,Fn=Fn−2+Fn−1,n=3,4,...F_1 = F_2 = 1, F_n = F_{n-2} + F_{n-1}, n = 3, 4, ... Assume pp is a prime greater than 33. With mm being a natural number greater than 33, find all nn numbers such that FnF_n is divisible by pmp^m.
Back to ProblemsView on AoPS