Archive for abc conjecture

the ABC conjecture

Posted in Books, University life with tags , , , , on November 27, 2012 by xi'an

Both Pour la Science and La Recherche, two French science magazines, had an entry this month on the abc conjecture! However, ABC being a common accronym, it is alas unrelated with my research theme. The abc conjecture is a number theory conjecture that states that if a and b are integers with no common factor and a small number of prime dividers, this does not hold for c=a+b. This is the abc triplet. (More precisely, the conjecture states that the quality of the triplet abc:

q(a,b,c) = \log c / \log \text{rad}(abc)

is larger than 1+ε for a finite number of triplets abc.) A proof of the conjecture by Shinichi Mochizuki was recently proposed, hence the excitment in the community. In La Recherche, I read that this conjecture is associated with an interesting computing challenge, namely to find the exhaustive collection of triplets with a quality more than a given bound 1+ε.

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