mersenneforum.org Another "solution for Fermat's Last Theorem"
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2013-11-06, 03:57   #1
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

925810 Posts
Another "solution for Fermat's Last Theorem"

Just for exercising the reading/parsing/error-finding skills, have a look at the cross-posted message (that was politely ignored by everyone) in primenumbers yahoo group.

I will only address the last statement therein (page 12):
Quote:
 Hence the reason I want to conclude the document with a proposition that for any positive integers xi, y and n the following statements is true y^n = x1^n + x2^n + x3^n … + xi^n if and only if i >= n.
It is curious that this is easily refuted by demonstration (with i=4 < n=5):
144^5 = 133^5+110^5+84^5+27^5 (due to found in the abstract of T.Womack's thesis; circa 1997).
Wiki tells us that this is the reinvented Euler's conjecture, and the disproof is due to L. J. Lander and T. R. Parkin (1966)

Last fiddled with by Batalov on 2013-11-06 at 04:42

 2013-11-06, 05:55 #2 TheMawn     May 2013 East. Always East. 11×157 Posts It's almost unfortunate that this was disproved. It would have been a very interesting theorem. I saw this video about it the other day. I really quite like Numberphile. Interesting stuff. It's just some information that most people here probably already know, but dumbed down a bit. http://www.youtube.com/watch?v=qiNcEguuFSA
 2013-11-06, 06:05 #3 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2×3×1,543 Posts The first line of this video is a grook by Piet Hein!
2013-11-06, 19:01   #4
R.D. Silverman

Nov 2003

164448 Posts

Quote:
 Originally Posted by Batalov Just for exercising the reading/parsing/error-finding skills, have a look at the cross-posted message (that was politely ignored by everyone) in primenumbers yahoo group. I will only address the last statement therein (page 12): It is curious that this is easily refuted by demonstration (with i=4 < n=5): 144^5 = 133^5+110^5+84^5+27^5 (due to found in the abstract of T.Womack's thesis; circa 1997). Wiki tells us that this is the reinvented Euler's conjecture, and the disproof is due to L. J. Lander and T. R. Parkin (1966)
And of course Noam Elkies constructed infinitely many counter-examples
for n = 4.

http://euler.free.fr/

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