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Topic: The Simpsons and the ABC conjecture :-)
Replies: 1   Last Post: Apr 7, 2013 4:31 PM

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David Bernier

Posts: 3,192
Registered: 12/13/04
Re: The Simpsons and the ABC conjecture :-)
Posted: Apr 7, 2013 4:31 PM
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On 04/07/2013 03:17 PM, fc3a501@uni-hamburg.de wrote:
> Remember the 3D adventure with the fake Fermat
> counter-example? Not so impressive in *absolute* terms,
> since you can easily give an infinite set of solutions
> to a^3+b^3-c^3=1. On the other hand, that example had
> ^12.
> Surely there has been work done on a^n+b^n-c^n="small"
> (I just have no idea how to google it :-) and it
> somehow relates to the ABC stuff.
> Mind to drop a link?
>


The ABC conjecture is about numbers a, b, c >=1,
integers, such that a + b = c.

There's a list of "best" (a, b, c) triplets:
those that come highest in a figure of merit
test:
"quality":

2 + (3^10)*109 = 23^5

due to E.R. , 1987

cf.:
< http://www.math.leidenuniv.nl/~desmit/abc/index.php?set=1 >

dave


--
Jesus is an Anarchist. -- J.R.



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