From: gerry@mpce.mq.edu.au (Gerry Myerson) Newsgroups: sci.math Subject: Re: Sums of cubes in many different ways Date: 3 Dec 1996 02:30:39 GMT In article <57uj64$pdi@news.ox.ac.uk>, mert0236@sable.ox.ac.uk (Thomas Womack) wrote: => => I also found a number the sum of two fourth powers in two different => ways, but not in three. => => ISTR that a solution for sixth powers hasn't yet been found, but this => may be out-of-date information. If you can find a number that's the sum of two 5th powers in two different ways, you'll be one ahead of the rest of us. If you can prove that there is no such number, you have a fine Ph.D. thesis. In fact, an open problem is to find a polynomial f(x) with integer coefficients together with a proof that there is no integer expressible in two ways as f(x) + f(y). Gerry Myerson (gerry@mpce.mq.edu.au) ============================================================================== From: rusin@vesuvius.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: Sums of cubes in many different ways Date: 4 Dec 1996 20:14:29 GMT In article , Gerry Myerson wrote: >If you can find a number that's the sum of two 5th powers in two different >ways, you'll be one ahead of the rest of us. 160^5 + (-150)^5 = (25 + sqrt(10145))^5 + (25 - sqrt(10145))^5 Hey, OK, so they're not rational, but they're pretty close. Do I get partial credit? :-) dave