About the ABC Conjecture and an alternative

  • Machiel van Frankenhuijsen


After a detailed discussion of the ABC Conjecture, we discuss three alternative conjectures proposed by Baker in 2004. The third alternative is particularly interesting, because there may be a way to prove it using the methods of linear forms in logarithms.

Key words

ABC Conjecture error term in the ABC Conjecture linear forms in logarithms 



We thank the referee for suggesting a number of important improvements to this paper. David Masser and Joseph Oesterlé kindly shared their recollection of the origins of the ABC Conjecture, and Hendrik Lenstra improved the paper by asking some insightful questions.


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsUtah Valley UniversityOremUSA

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