Re: are you interested in number theory AND programming

Newsgroups	comp.programming
Date	2020-06-17 00:55 -0700
References	(3 earlier) <87wo4bp8xo.fsf@bsb.me.uk> <f54e9e16-de6c-4c66-8b7e-fdf40ea290dbo@googlegroups.com> <87k10boswq.fsf@bsb.me.uk> <61c49983-9b6b-4f91-adf8-86aa33ada235o@googlegroups.com> <8b0924a3-e189-400c-825b-407a711f9947o@googlegroups.com>
Message-ID	<b78ddb91-e90d-45ae-80dd-fa6be6834450o@googlegroups.com> (permalink)
Subject	Re: are you interested in number theory AND programming
From	James Dow Allen <jdallen2000@yahoo.com>

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On Sunday, June 14, 2020 at 1:23:56 PM UTC+7, syedanw...@gmail.com wrote:
> This solves the following problem, for example :what is the smallest integer that can be written as a sum of three POSITIVE cubes in two different ways.

I see that your puzzle does solve this problem, involving "smallest."
But why?  It misses the *second* smallest such integer:
   1009 = 9^3 + 6^3 + 4^3 = 10^3 + 2^3 + 1^3
cannot be expressed with your a,b,c,d formula.

By the way, too bad you wrote "positive" instead of "non-negative." :-)
We miss out on the famous
    0 + 0 + 6^3 = 5^3 + 4^3 + 3^3


On Saturday, June 13, 2020 at 11:02:49 PM UTC+7, Ben Bacarisse wrote:
> The first 10 solution sets this program finds are:
> 
> (1,5) (2,3)
> (1,14) (3,7)
> (1,15) (2,10) (4,6)
...
The first triplet Ben found is closely related to the smallest number
which has *three* expressions as three positive cubes:
   5104 = 15^3 + 10^3 + 9^3 = 15^3 + 12^3 + 1^3 = 16^3 + 10^3 + 2^3
But the "Why?" of this isn't obvious to me.

Nitpick on terminology:  The quadruplets we are talking about are
SOLUTIONS, not "solution sets."  The Solution Set would be the
set of all possible solution quadruplets.

Jamesdowallen at Gmail

Thread

are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-12 02:25 -0700
  Re: are you interested in number theory AND programming root <NoEMail@home.org> - 2020-06-12 14:26 +0000
    Re: are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-12 19:34 -0700
      Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-13 11:16 +0100
        Re: are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-13 04:07 -0700
          Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-13 07:20 -0700
            Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-13 07:47 -0700
            Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-13 08:29 -0700
          Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-13 17:02 +0100
            Re: are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-13 23:11 -0700
              Re: are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-13 23:23 -0700
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-17 00:55 -0700
                Re: are you interested in number theory AND programming Richard Heathfield <rjh@cpax.org.uk> - 2020-06-17 09:30 +0100
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-17 02:32 -0700
                Re: are you interested in number theory AND programming Richard Heathfield <rjh@cpax.org.uk> - 2020-06-20 08:26 +0100
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-20 03:58 -0700
                Re: are you interested in number theory AND programming Richard Heathfield <rjh@cpax.org.uk> - 2020-06-20 14:55 +0100
                Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-17 23:11 +0100
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-20 04:44 -0700
                Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-20 06:27 -0700
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-21 17:31 -0700
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-22 02:00 -0700
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-22 05:34 -0700
                Re: are you interested in number theory AND programming root <NoEMail@home.org> - 2020-06-22 14:05 +0000
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-23 04:50 -0700
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-23 15:50 +0200
                Re: are you interested in number theory AND programming Chad <cdalten@gmail.com> - 2020-06-23 14:34 -0700
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-24 01:39 -0700
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-24 15:48 +0200
                Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-24 13:52 +0100
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-24 16:00 +0200
                Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-24 17:03 +0100
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-24 20:32 +0200
                Re: are you interested in number theory AND programming Chad <cdalten@gmail.com> - 2020-06-24 14:19 -0700
                Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-26 06:24 -0700
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 16:28 +0200
                Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-26 06:11 -0700
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-22 09:39 -0700
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-23 00:50 -0700
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-23 05:14 -0700
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-24 02:39 -0700
                Re: are you interested in number theory AND programming Richard Heathfield <rjh@cpax.org.uk> - 2020-06-25 20:48 +0100
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 08:48 +0200
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-26 01:25 -0700
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 11:10 +0200
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-26 03:56 -0700
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 13:34 +0200
                Re: are you interested in number theory AND programming Boris Dorestand <bdorestand@example.com> - 2020-06-27 11:22 -0300
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-27 17:50 +0200
                Re: are you interested in number theory AND programming Boris Dorestand <bdorestand@example.com> - 2020-06-27 13:42 -0300
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-07-04 18:44 -0700
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-07-09 19:51 -0700
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-07-10 05:32 -0700
                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-07-10 09:03 -0700
                Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-26 06:02 -0700
                Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-26 01:58 -0700
                Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 11:14 +0200
                Re: are you interested in number theory AND programming Richard Damon <Richard@Damon-Family.org> - 2020-06-26 13:10 -0400
                Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-26 06:12 -0700
          Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-13 23:28 +0200

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