## the ABC conjecture

**B**oth ** Pour la Science** and

*, 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*

**La Recherche***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*:

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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