tag:blogger.com,1999:blog-12535639.post7067057500601205686..comments2017-12-20T19:24:53.034-08:00Comments on Fermat's Last Theorem: Abel's Impossibility ProofLarry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-12535639.post-22114583250455275832017-08-09T23:05:50.429-07:002017-08-09T23:05:50.429-07:00Can we discuss Abel's impossibility proof with...Can we discuss Abel's impossibility proof with references to the findings in the links below?<br /><br />https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0ahUKEwjmhfD1-svVAhVrJ8AKHTKSD4UQFgg0MAI&url=https%3A%2F%2Fwww.rroij.com%2Fopen-access%2Fthe-bringjerrard-quintic-equation-its-algebraic-solution-byconversion-to-solvable-factorized-form-.php%3Faid%3D86068&usg=AFQjCNF5ysB5wjKJjpnK4GJ4nOC-gg2NLASamuelhttps://www.blogger.com/profile/17567021604595541064noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-23574598858802518592017-01-15T21:37:09.089-08:002017-01-15T21:37:09.089-08:00I think Theorem 2 - (2) needs some additional punc...I think Theorem 2 - (2) needs some additional punctuation.<br /><br />Perhaps the phrase: " where m is a prime number and R,p1,p2.. .are functions of this same form finitely nested at the deepest level each p,pi,R is a function of the coefficients of the general quintic equation." needs to begin a new sentence after "level".<br /><br />Also we can include "p" in the list "R, p1, p2".Bobo Cheverovskyhttps://www.blogger.com/profile/17774595689219106458noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-21301128888934328682015-09-05T07:50:06.709-07:002015-09-05T07:50:06.709-07:00Many thanks to Larry and his blog. I don't kn...Many thanks to Larry and his blog. I don't know how I could have worked through Dorrie's version of the theorem (third listed reference on the home page) without it (it requires more blog entries than just the current page).Sheryl Tannerhttps://www.blogger.com/profile/06667411175230571539noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-83436946145303683552015-09-05T07:45:06.113-07:002015-09-05T07:45:06.113-07:00E.T. Bell tells the story of how so many people we...E.T. Bell tells the story of how so many people were submitting papers on quintics alleging proof or disproof of their solvability, that Gauss trashed Abel's self-printed proof when he sent it to him as "another one of those monstrosities". It fell to Crelle and his new journal to give Abel his due, which turned out to make both of them famous.<br /><br />Since that time almost 200 years ago, Abel's theorem has been validated by so many people, and so many alternative proofs have been presented of it from different angles, that it seems impossible that it could be disproven now.Sheryl Tannerhttps://www.blogger.com/profile/06667411175230571539noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-5698371117816474812015-09-05T07:25:28.461-07:002015-09-05T07:25:28.461-07:00The note by Buya is incorrect. The product of the...The note by Buya is incorrect. The product of the two factors gives a nonzero x^3 term when multiplied out. Another way to show that the quintic does not factor as shown is to substitute a value for x into both equations. For example, with x=3 we get 241 for the quintic, but 227.5-70.1i for the product of the quadratic and cubic terms.Sheryl Tannerhttps://www.blogger.com/profile/06667411175230571539noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-72765263993627373292014-01-15T05:14:41.378-08:002014-01-15T05:14:41.378-08:00consider the quintic equation x^5-x+1=0. It can be...consider the quintic equation x^5-x+1=0. It can be factorized to <br />[x^2+x+2/(1+i√3)]<br />[x^3-x^2+(3-i√3)/(1+i√3) x+(1+i√3)/2]=0. This means it is a reducible quintic and it has radical solution. Similarly all other quintics can be reduced to auxiliary cubic and quadratic factors. This disproves Abel impossibility theorem.<br />Samuel Bonaya BuyaSamuel Bonaya Buyahttps://www.blogger.com/profile/13888621400263034065noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-59159735650714681892014-01-15T05:10:08.555-08:002014-01-15T05:10:08.555-08:00consider the quintic equation x^5-x+1=0. It can be...consider the quintic equation x^5-x+1=0. It can be factorized to <br />[x^2+x+2/(1+i√3)]<br />[x^3-x^2+(3-i√3)/(1+i√3) x+(1+i√3)/2]=0. This means it is a reducible quintic and it has radical solution. Similarly all other quintics can be reduced to auxiliary cubic and quadratic factors. This disproves Abel impossibility theorem.<br />Samuel Bonaya BuyaSamuel Bonaya Buyahttps://www.blogger.com/profile/13888621400263034065noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-36837099675730953332013-11-17T04:54:58.790-08:002013-11-17T04:54:58.790-08:00Again what would the margin of error in taking x=-...Again what would the margin of error in taking x=-(6822150561/5000000000) as the root of x^5-2x+2=0? Samuel Bonaya BuyaSamuel Bonaya Buyahttps://www.blogger.com/profile/13888621400263034065noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-72245904051247053782013-11-16T12:16:53.638-08:002013-11-16T12:16:53.638-08:00Can anyone determine the margin of error of x1=-( ...Can anyone determine the margin of error of x1=-( 70038238698/60000000000) as one of the roots of x^5-x+1=0? Samuel Bonaya BuyaSamuel Bonaya Buyahttps://www.blogger.com/profile/13888621400263034065noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-4971335228815492042010-08-22T16:33:02.504-07:002010-08-22T16:33:02.504-07:00Hi Dr. MacIntyre,
Thanks very much for the feedba...Hi Dr. MacIntyre,<br /><br />Thanks very much for the feedback on my blog.<br /><br />I've added the link to Corollary 1.1. Thanks very much for reporting this issue.<br /><br />Cheers,<br /><br />-LarryLarry Freemanhttps://www.blogger.com/profile/06906614246430481533noreply@blogger.comtag:blogger.com,1999:blog-12535639.post-17063376268407072382010-08-22T09:43:04.929-07:002010-08-22T09:43:04.929-07:00May I say how impressed I am by your presentation....May I say how impressed I am by your presentation.<br /><br />I speak as someone whose math theory is rusty - very, very rusty.<br /><br />So all the help and stepping stones you offer are invaluable.<br /><br />Even so, sometimes my slowness and misunderstandings can still wreck my progress!<br /><br />I've got to Step 13, your Wed 1st Oct 2008 post, and clicked on 'here' to find Corollary 1.1 (it doesn't appear to be on the given page)<br /><br />But there was no link!<br /><br />Can you possibly help me by telling me which blog post date Corollary 1.1 falls under? <br /><br />With great gratefulness,<br /><br /><br />Dr. Ian MacIntyre (retd) at n_mcntyr@yahoo.co.ukmachttps://www.blogger.com/profile/11722772823535639360noreply@blogger.com