My Math Forum divisibility proof question
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June 29th, 2016, 12:26 PM   #1
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divisibility proof question

please see image attached.

for part (i), i used an induction. I wasn't bothered by this part.

For part (ii), i managed to do the first part. The second part involves proving that S is divisible by different things depending on the even/odd status of n, which i was also fine with.

The past part, proving S is divisible by 1+...+n has me completely stuck. I have the mark scheme, and am trying to decipher it like a foreign newspaper. My worry is that by just inferring from the answer, i won't really get it. All help appreciated
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 June 29th, 2016, 02:35 PM #2 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 551 This is an off the cuff reply. You will likely need to use your previous results to prove the final result. Clearly n is even or odd. So one of the prior results will apply. You have not shown what you got in the earlier stages so it is very difficult to show HOW they apply.
July 3rd, 2016, 02:28 AM   #3
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the image attatched is my set of answers, up to the last part.
As you can see, I've figured out that S has factors of (n+1) and (n+1)/2, depending on whether n is odd or even. I used the results about S being divisible by n and n/2 to deduce this.

My problem now is proving that for all n, S is divisible by n(n+1)/2. For this, I am not sure. It looks like I have half of it in both cases...
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