Example

Prove that $11^n-6$ is divisible by 5, $\forall : n \in \mathbb{N}$.

_(A number is said to be divisible by 5 if it can be written as $5c$, for some integer $c$.)

Base Case
$11^1 - 6 = 5 = 5 \cdot 1$, therefore the base case holds.

Induction Hypothesis
Assume $11^k - 6$ is divisible by 5, for some arbitrary $k$.

Induction Step