From: Richard Pinch <rgep@cam.ac.uk>
Newsgroups: sci.math
Subject: Re: abc - conjecture (experiment)
Date: Fri, 06 Mar 1998 14:38:27 +0000

Branka Lasic wrote:
> 
> Let a,b,c be nonzero relatively prime integers such that a + b = c.
> 
> Define the radical of x to be the product of the distinct primes dividing
> x.
> 
> Let
> 
> L(a,b)=log(a+b) / log rad(a*b*(a+b))
> 
> I have found max value of L to be
> 
> L(1,4374) = log 4375 / log(2*3*5*7) = 1.5678...

From  Maths Reviews 94g:11021 Browkin, J.; Brzezi\'nski, J.
Some remarks on the $abc$-conjecture.
Math. Comp. 62 (1994), no. 206, 931--939.

"a table of 90 extreme examples for the $abc$-conjecture is presented, 
all with $L(a,b,c)>1.4$. The largest known value is 1.629912, reached 
by $2+3^{10}109=23^5$, an example due to E. Reyssat."

Also mentioned in the review are:
L(1,4374,4375)=1.567887
L(1,2400,2401)=1.455673
L(3,125,128)=1.426565
-- 
Richard Pinch		Queens' College, Cambridge
rgep@cam.ac.uk		http://www.dpmms.cam.ac.uk/~rgep
Looking for a job from Oct'98: 
		http://www.dpmms.cam.ac.uk/~rgep/cv.html