Wednesday, 2 August 2017

elementary number theory - A sequence divisible by 9

I was trying to solve this series by mathematical induction for every n from N : un=n4n+1(n+1)4n+1 is divisible by 9.



The initiation was pretty easy, but I only managed to prove un+1=3k while k is an integer and I don't think if it's divisible by 3 implies that it is divisible by 9 ; is it ? if not how can I proceed to prove the divisibility ? by mod maybe? thanks in advance for your answer

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