21 Jun 2013

Prize Maths Quiz: Sum of Divisors (PMQ24)

Omar Khayyam (1048-1131)
Let S(n) be the sum of the positive divisors of the positive integer n, including both 1 and n itself.

Find all values of n such that S(n) = 120 and prove that there are no others.


In most countries, mathematics competitions tend to be multiple-choice answers in the first round, then numerical answers in the follow-up round. But if you make it beyond these rounds, the questions become longer and harder and you will need to show your full solutions.

Finding an answer is sometimes the easiest part; showing that you have found all the answers is often the hardest part. With this in mind, it is worth doing the above question by hand as it will also be the way you can show that you have found all the solutions.


You may discuss the question below, but no full answers, please, until the competition has closed!

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How to Enter

Send your complete solution by email to pmq24poisson@giftedmaths.comThis email address shall be removed after the competition closes to avoid spam. This PMQ24 competition closes on MONDAY 24 June at 23:59 GMT - one extra weekday from now on.

The Prize

The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR. The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.

Quick Rules

Look at the expanded rules on our PMQ page.
Anybody can enter our Prize Maths Quiz; adults and students.
Use the official server clock in the right column to avoid late entries.
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DO NOT submit your entries to the comments section at the bottom of this post.
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Enjoy the challenge!
Send us your solution! You can't win if you don't participate.
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