abc conjecture and Fermat's Last Theorem

jasong · 2012-10-19, 23:09

I, by total accident, saw a video on Youtube about a possible proof of the abc conjecture. I never knew it before, but the guy claimed that people originally thought the solution to Fermat's Last Theorem was to prove the abc conjecture and apply that solution to Fermat's Last Theorem. I probably phrased that badly, but...

If anybody knows what the connection is between the abc conjecture and Fermat's Last Theorem, could this proof, if it truly is a proof, affect the effectiveness of primality tests, or maybe even come up with a new way of doing things faster?

I know that there are quite a few trolls on here that will say,"Sure, anything's POSSIBLE, trololol." But it does make me wonder.

Dubslow · 2012-10-19, 23:51

http://www.mersenneforum.org/showthread.php?t=17171

Fermat's Last Theorem is a consequence of the abc conjecture.

CRGreathouse · 2012-10-20, 21:02

Quote:

Originally Posted by Dubslow

Fermat's Last Theorem is a consequence of the abc conjecture.

For large enough exponents, that is.

jasong · 2012-10-24, 08:45

If it is confirmed to be a proof, won't it affect our ability to find titanic primes? Are there methods out there that aren't used simply because they haven't been rigorously proven?

2012-10-19, 23:09	#1
jasong "Jason Goatcher" Mar 2005 3507₁₀ Posts	abc conjecture and Fermat's Last Theorem I, by total accident, saw a video on Youtube about a possible proof of the abc conjecture. I never knew it before, but the guy claimed that people originally thought the solution to Fermat's Last Theorem was to prove the abc conjecture and apply that solution to Fermat's Last Theorem. I probably phrased that badly, but... If anybody knows what the connection is between the abc conjecture and Fermat's Last Theorem, could this proof, if it truly is a proof, affect the effectiveness of primality tests, or maybe even come up with a new way of doing things faster? I know that there are quite a few trolls on here that will say,"Sure, anything's POSSIBLE, trololol." But it does make me wonder.

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2012-10-19, 23:51	#2
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 1110000110101₂ Posts	http://www.mersenneforum.org/showthread.php?t=17171 Fermat's Last Theorem is a consequence of the abc conjecture.

2012-10-24, 08:45	#4
jasong "Jason Goatcher" Mar 2005 DB3₁₆ Posts	If it is confirmed to be a proof, won't it affect our ability to find titanic primes? Are there methods out there that aren't used simply because they haven't been rigorously proven?