This guy's thesis has an approachable explanation of the conjecture, as well as some of the interesting theorems that it implies (including an asymptotic version of Fermat's Last Theorem):
there's an apostrophe before the "s" in "Masters" that is stripped out by the HN code for some reason. either add that or go to http://jeffreypaulwheeler.com/ and select the link "The abc Conjecture" near the start of "Papers Section".
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This guy's thesis has an approachable explanation of the conjecture, as well as some of the interesting theorems that it implies (including an asymptotic version of Fermat's Last Theorem):
http://jeffreypaulwheeler.com/Masters%20Thesis.pdf
Corrected link: http://jeffreypaulwheeler.com/Master%27s%20Thesis.pdf
404
there's an apostrophe before the "s" in "Masters" that is stripped out by the HN code for some reason. either add that or go to http://jeffreypaulwheeler.com/ and select the link "The abc Conjecture" near the start of "Papers Section".