a^5 + b^5 + c^5 = d^5 + e^5 + f^5 = x^5 + y^5 + z^5
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From: Dan Cass on 3 Dec 2009 03:29 > In article > <1060668259.58373.1259609120702.JavaMail.root(a)gallium. > mathforum.org>, > master1729 <tommy1729(a)gmail.com> wrote: > > > let a b c d e f x y z be distinct positive > integers. > > > > a^5 + b^5 + c^5 = d^5 + e^5 + f^5 = x^5 + y^5 + z^5 > > > > solve that diophantine equation. > > People may be interested to know that Swinnerton-Dyer > gave > a parametric solution to a^5 + b^5 + c^5 = d^5 + e^5 > + f^5 > in Proc Camb Phil Soc 48 (1952) 516-518. > > -- > Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for > email) If one takes Swinnerton-Dyer's parametric solution, and replaces the parameters by complex variables, then separates real and imaginary parts, one finds either infinitely many solutions, or else one finds one might as well wrinkle the paper up and throw it away.
From: master1729 on 6 Dec 2009 07:29 Dan Cass wrote : > > In article > > > <1060668259.58373.1259609120702.JavaMail.root(a)gallium. > > > mathforum.org>, > > master1729 <tommy1729(a)gmail.com> wrote: > > > > > let a b c d e f x y z be distinct positive > > integers. > > > > > > a^5 + b^5 + c^5 = d^5 + e^5 + f^5 = x^5 + y^5 + > z^5 > > > > > > solve that diophantine equation. > > > > People may be interested to know that > Swinnerton-Dyer > > gave > > a parametric solution to a^5 + b^5 + c^5 = d^5 + > e^5 > > + f^5 > > in Proc Camb Phil Soc 48 (1952) 516-518. > > > > -- > > Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for > > email) > > If one takes Swinnerton-Dyer's parametric solution, > and replaces the parameters by complex variables, > then separates real and imaginary parts, > one finds either infinitely many solutions, > or else one finds one might as well wrinkle the > paper > up and throw it away. what are you trying to say here ?
From: Dan Cass on 8 Dec 2009 02:30 > Dan Cass wrote : > > > > In article > > > > > > <1060668259.58373.1259609120702.JavaMail.root(a)gallium. > > > > > > mathforum.org>, > > > master1729 <tommy1729(a)gmail.com> wrote: > > > > > > > let a b c d e f x y z be distinct positive > > > integers. > > > > > > > > a^5 + b^5 + c^5 = d^5 + e^5 + f^5 = x^5 + y^5 > + > > z^5 > > > > > > > > solve that diophantine equation. > > > > > > People may be interested to know that > > Swinnerton-Dyer > > > gave > > > a parametric solution to a^5 + b^5 + c^5 = d^5 + > > e^5 > > > + f^5 > > > in Proc Camb Phil Soc 48 (1952) 516-518. > > > > > > -- > > > Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u > for > > > email) > > > > If one takes Swinnerton-Dyer's parametric > solution, > > and replaces the parameters by complex variables, > > then separates real and imaginary parts, > > one finds either infinitely many solutions, > > or else one finds one might as well wrinkle the > > paper > > up and throw it away. > > what are you trying to say here ? Sorry, it was a joke response. Mainly because I see no idea how to solve it...
From: master1729 on 8 Dec 2009 04:43 Gerry Myerson wrote : > In article > <1060668259.58373.1259609120702.JavaMail.root(a)gallium. > mathforum.org>, > master1729 <tommy1729(a)gmail.com> wrote: > > > let a b c d e f x y z be distinct positive > integers. > > > > a^5 + b^5 + c^5 = d^5 + e^5 + f^5 = x^5 + y^5 + z^5 > > > > solve that diophantine equation. > > People may be interested to know that Swinnerton-Dyer > gave > a parametric solution to a^5 + b^5 + c^5 = d^5 + e^5 > + f^5 > in Proc Camb Phil Soc 48 (1952) 516-518. > > -- > Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for > email) maybe you can give the parametric solution here explicitly ? for once , lets - for the heck of it - post something explicitly on sci.math without a reference. how exciting that would be. or is that illegal or something ? tommy1729
From: Gerry Myerson on 8 Dec 2009 18:10 In article <1032884984.26267.1260301429799.JavaMail.root(a)gallium.mathforum.org>, master1729 <tommy1729(a)gmail.com> wrote: > Gerry Myerson wrote : > > > In article > > <1060668259.58373.1259609120702.JavaMail.root(a)gallium. > > mathforum.org>, > > master1729 <tommy1729(a)gmail.com> wrote: > > > > > let a b c d e f x y z be distinct positive > > integers. > > > > > > a^5 + b^5 + c^5 = d^5 + e^5 + f^5 = x^5 + y^5 + z^5 > > > > > > solve that diophantine equation. > > > > People may be interested to know that Swinnerton-Dyer > > gave a parametric solution to a^5 + b^5 + c^5 = d^5 + e^5 + f^5 > > in Proc Camb Phil Soc 48 (1952) 516-518. > > maybe you can give the parametric solution here explicitly ? > > for once , lets - for the heck of it - post something explicitly on sci.math > without a reference. > > how exciting that would be. > > or is that illegal or something ? For once, go look something up yourself. -- Gerry Myerson (gerry(a)maths.mq.edi.ai) (i -> u for email)
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