
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 29th, 2016, 12:26 PM  #1 
Member Joined: Jan 2016 From: United Kingdom Posts: 35 Thanks: 0  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 
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 
Member Joined: Jan 2016 From: United Kingdom Posts: 35 Thanks: 0 
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... 

Tags 
divisibility, proof, question, tricky 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Proof for divisibility  MageKnight  Number Theory  5  March 10th, 2014 01:40 PM 
Show that...(Divisibility proof)  usermind  Number Theory  1  April 18th, 2012 09:30 AM 
Subset Divisibility proof  jstarks4444  Number Theory  1  October 31st, 2011 02:30 PM 
Prime Divisibility Proof  jstarks4444  Number Theory  0  March 15th, 2011 03:24 PM 
Power Divisibility Proof  jstarks4444  Number Theory  8  March 9th, 2011 06:21 AM 