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From: matt@oddjob.UUCP
Newsgroups: net.math
Subject: Re: A number theory problem
Message-ID: <946@oddjob.UUCP>
Date: Sun, 25-Aug-85 21:38:44 EDT
Article-I.D.: oddjob.946
Posted: Sun Aug 25 21:38:44 1985
Date-Received: Tue, 27-Aug-85 00:46:27 EDT
References: <388@aero.ARPA>
Reply-To: matt@oddjob.UUCP (Matt Crawford)
Organization: U. Chicago, Astronomy & Astrophysics
Lines: 15

>My question is, what is the smallest number that can be written as the
>sum of two cubes in THREE different ways? Does one exist?
>
>                                   Bill Sinclair (asbestos Willie)

The smallest 3-way sum of cubes is 87539319.

Misspending part of a summer on this sort of question led me to
observe that the number 221*5^n seems to be expressible as a sum
of two squares 2n+2 different ways for n through at least 10 or
so.  Is it true for all n?  If so, why?
_____________________________________________________
Matt		University	crawford@anl-mcs.arpa
Crawford	of Chicago	ihnp4!oddjob!matt