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The polymath wiki happened to have a page on the ABC conjecture back in 2009 (as part of the Polymath4 project).  It now has a number of sections that collect links and other information on the series of papers by Mochizuki claiming to prove that conjecture.  Of course, it doesn't yet have the answer to the question most eagerly sought - namely, "is the proof correct?" - but hopefully it will do so in the future.  (And, of course, being a wiki, further updates and corrections by interested readers would of course be welcome.)
The abc conjecture asserts, roughly speaking, that if a+b=c and a,b,c are coprime, then a,b,c cannot all be too smooth; in particular, the product of all the primes dividing a, b, or c has to exceed c...
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