Prove that n^3 +11n is divisible by 6
Theorem: n3+11nn^{3}+11n is divisible by 6 for all n∈ℤn\in\mathbb{Z} We use proof by induction. Let’s have the induction hypothesis stated as follows: Base case: For n=0n=0, we have 03+11.0=00^{3}+11.0=0, and 6|06 \mid 0. So for n=0n=0, P(n)P(n) is true. Inductive Step: We need to proof that by assuming P(n)P(n) is true, P(n+1)P(n+1) is true, or … More Prove that n^3 +11n is divisible by 6