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