Using the Principle of Well Order, show that for all $n \in N$ it holds that $4^n -1$ is divisible by 3. I have already defined the set of counterexamples $C$, then I proved that for $n=1$ the proposition holds. Then I established that $c$ (the minimum element of $C$) must be the successor of some natural number $k$ such that $c=k+1$ and therefore $k=c-1$, so that: $4^k -1$ is divisible by 3, apply the definition of divisibility to this last statement: $4^k -1=3m$, therefore, $4^{c-1} -1$ is divisible by 3.
Then, using the Division Algorithm, I can represent $4^c -1=3m+r$, from here I don't know how to continue.