From: gerry@mpce.mq.edu.au (Gerry Myerson)
Newsgroups: sci.math
Subject: Re: 4/1033
Date: Thu, 08 Oct 1998 15:59:26 +1100

In article <19981007213153.16560.00008226@ng93.aol.com>, tatui@aol.com
(Tatui) wrote:

> How do you write 4/1033 as the sum of three egyptian fractions.
> i.e. 4/1033 = 1/a +1/b + 1/c ??

By trial-and-error. 

First take a as small as possible subject to 1/a < 4/1033, that is, 
take a just bigger than 1033/4. Compute 4/1033 - 1/a and see whether 
you can write it as 1/b + 1/c for some b & c --- that shouldn't be 
to hard to decide. If you can, you're done. 

If you can, increase a by 1, and iterate until done. 

For those who have never seen this before, Erdos & Straus conjectured 
that for all n > 5 there exist positive integers a, b, c such that 
4/n = 1/a + 1/b + 1/c. The conjecture has never been settled, but 
it has been verified out to way past 1033. Thus, my procedure terminates. 

Gerry Myerson (gerry@mpce.mq.edu.au)
==============================================================================

From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: 4/1033
Date: 8 Oct 1998 04:19:12 GMT

In article <19981007213153.16560.00008226@ng93.aol.com>,
Tatui <tatui@aol.com> wrote:
>
>How do you write 4/1033 as the sum of three egyptian fractions.
>i.e. 4/1033 = 1/a +1/b + 1/c ??

[a,b,c]=[282, 3099, 291306].

This is an example of Erdos's  "4/n"  problem. See
Guy, "Unsolved Problems in Number Theory", section D11.

dave