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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 ...
Inter-universal Teichmüller theory is a continuation of Mochizuki's previous work in arithmetic geometry. This work, which has been peer-reviewed and well received by the mathematical community, includes major contributions to anabelian geometry, and the development of p-adic Teichmüller theory, Hodge–Arakelov theory and Frobenioid categories.
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 ...
abc conjecture The abc conjecture of Masser and Oesterlé attempts to state as much as possible about repeated prime factors in an equation a + b = c. For example 3 + 125 = 128 but the prime powers here are exceptional. Arakelov class group The Arakelov class group is the analogue of the ideal class group or divisor class group for Arakelov ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Joseph Oesterlé (born 1954) is a French mathematician who, along with David Masser, formulated the abc conjecture which has been called "the most important unsolved problem in diophantine analysis". [2] [3] He is a member of Bourbaki. [4]