ABC conjecture

The ABC conjectureMathworldPlanetmath states that given any ϵ>0, there is a constant κ(ϵ) such that


for all mutually coprime integers A, B, C with A+B=C, where rad is the radicalPlanetmathPlanetmath of an integer. This conjecture was formulated by Masser and Oesterlé in 1980.

The ABC conjecture is considered one of the most important unsolved problems in number , as many results would follow directly from this conjecture. For example, Fermat’s Last Theorem could be proved (for sufficiently large exponents) with about one page worth of proof.

Further Reading Amazing ABC Conjecture — an article on the ABC conjecture by Ivars Peterson. ABC’s of Number TheoryMathworldPlanetmathPlanetmath — an article on the ABC conjecture by Noam Elkies. (PDF file)

Title ABC conjecture
Canonical name ABCConjecture
Date of creation 2013-03-22 11:45:23
Last modified on 2013-03-22 11:45:23
Owner yark (2760)
Last modified by yark (2760)
Numerical id 21
Author yark (2760)
Entry type Conjecture
Classification msc 11A99
Classification msc 55-00
Classification msc 82-00
Classification msc 83-00
Classification msc 81-00
Classification msc 18-00
Classification msc 18C10