Wednesday, 19 August 2015

discrete mathematics - Prove n3+7n+3 is divisible by 3 for all integers n ≥ 0




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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