The statement I'm trying to prove is:
n3+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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