On Tue, Jun 01, 2004 at 08:22:41PM +0100, Jon Perry wrote:
I've not seen this anywhere else, can we generalize the abc conjecture into something whereby;
f=a+b+c+d+e
or any number of variables, and a form of the original abc conjecture still exists?
A google for 'abc conjecture' gives the page http://www.math.unicaen.fr/~nitaj/abc.html which has a generalized conjecture as you ask for: The n-term abc conjecture for integers. In 1994, Browkin and Brzezinski [Br-Brz] proposed the following conjecture. Given any integer n > 2 and any eps > 0, there exists a constant C(n,eps), such that for all integers a1, ..., an with a1+...+ an=0, gcd( a1,..., an)=1 and no proper zero subsum, we have max(|a1|,...,|an|) <= C(n,eps)*(rad(a1 � ... � an))^(2n-5+eps). Peace, Dylan