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The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. [ 1 ] [ 2 ] It is stated in terms of three positive integers a , b {\displaystyle a,b} and c {\displaystyle c} (hence the name) that are relatively prime and satisfy a ...
The most striking claimed application of the theory is to provide a proof for various outstanding conjectures in number theory, in particular the abc conjecture. Mochizuki and a few other mathematicians claim that the theory indeed yields such a proof but this has so far not been accepted by the mathematical community.
Mochizuki proved Grothendieck's conjecture on anabelian geometry in 1996. He was an invited speaker at the International Congress of Mathematicians in 1998. [13] In 2000–2008, he discovered several new theories including the theory of frobenioids, mono-anabelian geometry and the etale theta theory for line bundles over tempered covers of the Tate curve.
Conjecture Field Comments Eponym(s) Cites 1/3–2/3 conjecture: order theory: n/a: 70 abc conjecture: number theory: ⇔Granville–Langevin conjecture, Vojta's conjecture in dimension 1 ⇒Erdős–Woods conjecture, Fermat–Catalan conjecture Formulated by David Masser and Joseph Oesterlé. [1] Proof claimed in 2012 by Shinichi Mochizuki: n/a ...
In 2012, the Japanese mathematician Shinichi Mochizuki released online a series of papers in which he claims to prove the abc conjecture. Despite the publication in a peer-reviewed journal later, his proof has not been accepted as correct in the mainstream mathematical community. [23]
Pages in category "Abc conjecture" The following 29 pages are in this category, out of 29 total. This list may not reflect recent changes. A. ABC@Home; Abc conjecture; B.
abc conjecture The abc conjecture says that for all ε > 0, there are only finitely many coprime positive integers a, b, and c satisfying a+b=c such that the product of the distinct prime factors of abc raised to the power of 1+ε is less than c. adele Adele ring algebraic number
The abc conjecture roughly states that if three positive integers a, b and c (hence the name) are coprime and satisfy a + b = c, then the radical d of abc is usually not much smaller than c. In particular, the abc conjecture in its most standard formulation implies Fermat's last theorem for n that are sufficiently large.