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 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