11510 - Erdös Unit Fractions

All about problems in Volume 115. If there is a thread about your problem, please use it. If not, create one with its number in the subject.

Moderator: Board moderators

Post Reply
zhouerjin
New poster
Posts: 5
Joined: Wed Oct 01, 2008 4:52 pm

11510 - Erdös Unit Fractions

Post by zhouerjin » Thu Oct 02, 2008 12:27 pm

I don't know how to solve this problem...I need help...

Leonid
Experienced poster
Posts: 146
Joined: Thu Dec 22, 2005 5:50 pm
Contact:

Re: 11510 - Erdös Unit Fractions

Post by Leonid » Thu Oct 02, 2008 5:26 pm

You may apply this lemma in your approach:

Code: Select all

Suppose that n and d are relatively prime positive integers. Then n/d is the sum of two unit fractions if and only if there are positive integer divisors A and B of d such that A+B is divisible by n.
You may also read this to improve the performance of your solution.

Bruno
New poster
Posts: 22
Joined: Thu Oct 01, 2009 9:03 pm

Re: 11510 - Erdös Unit Fractions

Post by Bruno » Fri Oct 30, 2009 1:38 pm

I apparently found a very quick way to find x y and z with even numbers and odd numbers in the form 3 + 4k, all based on the 4/n thing that you can write it as a form of 2 unit fractions. But I would like to know how to calculate for prime numbers !

Post Reply

Return to “Volume 115 (11500-11599)”