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The abc conjecture in number theory was first formulated by Joseph Oesterlé and David Masser in 1985.

It states that for any \varepsilon > 0 there exists a constant C_{\varepsilon} > 0 , such that for every triple of coprime positive integers a, b, c satisfying a + b = c, we have

c < C_{\varepsilon} \operatorname{rad}(abc)^{1+\epsilon},

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Just finished writing up some results on the ABC Conjecture and isogenies between Frey curves for my program at MSRI next summer.
edraygoins (Edray Herber Goins, ) Tue, 10 Nov 2009 17:51:15 -0000
Just finished writing up some results on the ABC Conjecture and isogenies between Frey curves for my program at MSRI next summer.

 
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A New Extreme ABC-example - Explanation of an example with quality 1.920859, found by Benne de Weger and Niklas Broberg.

Good ABC-Ratios - Known ratios greater than 1.4, compiled by Andrej Rosenheinrich, based on a table of ratios by Abderrahmane Nitaj.

Introduction to the ABC Conjecture - Slides by Barry Mazur.

MUG: ABC-conjecture - Maple code to illustrate the conjecture discussed and refined.

The ABC Conjecture - Maintained by Abderrahmane Nitaj.

The Amazing ABC Conjecture - Article by Ivars Peterson.

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