Find out how many positive integers $n$ not larger than $2009$ exist such that the last digit of $n^{20}$ is $1$.
Problem
Source: Paraguayan National Olympiad 2009, Level 3, Problem 3
Tags: number theory proposed, number theory
Source: Paraguayan National Olympiad 2009, Level 3, Problem 3
Tags: number theory proposed, number theory
Find out how many positive integers $n$ not larger than $2009$ exist such that the last digit of $n^{20}$ is $1$.