Thread: Divisibility by 9

Prove that, for any positive integer



is divisible by 9.

denotes the integer part of .

I wasn't sure how to go about this question, any help?

Originally Posted by CuriosityCabinet

Prove that, for any positive integer



is divisible by 9.

denotes the integer part of .

I wasn't sure how to go about this question, any help?

There are various methods you can try. How about using induction? Another way is to solve it on a case by case analysis. Prove it for the three cases n = 3k, n = 3k +1 and n = 3k + 2. The latter method gets rid of the greatest integer function and makes the solution pretty clear