Divisibility Mathematical Induction Help Could you please help me with this question prove that $\displaystyle5^n + 2\cdot(11)^n$ is a multiple of $3$.
Thanks

Base case: n = 0
$$5^0+2(11)^0 = 1 + 2 = 3$$
Inductive case: suppose the hypothesis holds for $n\le k$
$$5^{k+1} + 2(11)^{k+1}= 5 5^{k} + (6+5)2(11)^{k}=\cdots$$
