discrete mathematics - Prove $n^3 + 7n + 3$ is divisible by 3 for all integers n ≥ 0

Wednesday 19 August 2015

The statement I'm trying to prove is:

$n^3 + 7n + 3$ is divisible by 3 for all integers n ≥ 0

I eventually need to prove $(k + 1)^3 + 7(k + 1) + 3$ is divisible by 3.

I don't really understand how to deal with $k + 1$, so I'm a little lost.

I've know that the base case of P(0) is true, but I'm not sure about proving the inductive case.

Answer

The statement is not true. Take $n=1$ as a counter example.

Since it's not true, you won't manage to prove it (by induction or otherwise).

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