Example: Prove that $ \forall n\in{\mathbb N}, n^5-n $ is a multiple of n.
Base case: n=0... 0^5=0 as we want
Inductive step: Assume that 5 divides $ n^5-n $ and show that 5 divides $ (n+1)^5-(n+1) $
Example: Prove that $ \forall n\in{\mathbb N}, n^5-n $ is a multiple of n.
Base case: n=0... 0^5=0 as we want
Inductive step: Assume that 5 divides $ n^5-n $ and show that 5 divides $ (n+1)^5-(n+1) $