I want to show that all positive even integers have even number of digit “$1$” in their triadic representation.
An even number is of the form $n = 2k$ with $k\in \mathbb{Z}$.
To find the triadic representation we do the Euclidean division of the number $n$ and $3$ and we consider the remainders to get the triadic representation, right?
First we do $n : 3 = 2k : 3$. Then we have to take cases if $k$ is a multiple of $3$ or not, right?