Determine all finite non-empty sets S of positive integers satisfying

(i + j)/gcd(i, j) is an element of S for all i, j in S.

The gcd(i, j) is the greatest common divisor of i and j.

[APMO 2004 Q1][edited so easier to read online]

**Feel free to comment, ask questions and even check your answer in the comments box below powered by**~~Disqus~~ Google+.

**}**

**This space is here to avoid seeing the answers before trying the problem!**

*}*

**If you enjoy using this website then please consider making a donation - every little helps :-)**

**You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.**

**Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..**

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.

## No comments:

## Post a Comment