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.

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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...

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Re: 11510 - Erdös Unit Fractions

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

You may apply this lemma in your approach:

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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.

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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 !

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