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...

Szpiro's conjecture relates to the conductor and the discriminant of an elliptic curve. In a slightly modified form, it is equivalent to the well-known abc conjecture...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b,...

The Beal conjecture is the following conjecture in number theory: Unsolved problem in mathematics If A x + B y = C z {\displaystyle A^{x}+B^{y}=C^{z}}...

x^{\lambda n}} uniformly in m and n. The general conjecture would follow from the ABC conjecture. Pillai's conjecture means that for every natural number n, there...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem...

from non-mathematicians due to claims it provides a resolution of the abc conjecture. Shinichi Mochizuki was born to parents Kiichi and Anne Mochizuki. When...

Vojta's conjecture is a conjecture introduced by Paul Vojta (1987) about heights of points on algebraic varieties over number fields. The conjecture was motivated...

to provide a proof for various outstanding conjectures in number theory, in particular the abc conjecture. Mochizuki and a few other mathematicians claim...

theory, the Fermat–Catalan conjecture is a generalization of Fermat's Last Theorem and of Catalan's conjecture. The conjecture states that the equation...

Fermat's Last Theorem Mordell conjecture Euler's sum of powers conjecture abc Conjecture Catalan's conjecture Pillai's conjecture Hasse principle Diophantine...

integers n {\displaystyle n} . n conjecture: a generalization of the abc conjecture to more than three integers. abc conjecture: for any ε > 0 {\displaystyle...

Gauss–Manin connection may give some important hints for Vojta's conjecture, ABC conjecture and so on; in 2012, he published his Inter-universal Teichmuller...

prime}}}p} The radical plays a central role in the statement of the abc conjecture. Radical numbers for the first few positive integers are 1, 2, 3, 2...

Ribet's theorem (earlier called the epsilon conjecture or ε-conjecture) is part of number theory. It concerns properties of Galois representations associated...

number theory, the n conjecture is a conjecture stated by Browkin & Brzeziński (1994) as a generalization of the abc conjecture to more than three integers...

a French mathematician who, along with David Masser, formulated the abc conjecture which has been called "the most important unsolved problem in diophantine...

Look up ABC, abc, A.B.C., or ABCs in Wiktionary, the free dictionary. ABC are the first three letters of the Latin script. ABC or abc may also refer to:...

statement was known as the Taniyama–Shimura conjecture, Taniyama–Shimura–Weil conjecture, or the modularity conjecture for elliptic curves. The theorem states...

numbers as well as more general subjects such as number fields and the abc conjecture. As of 2024[update], the only known Wieferich primes are 1093 and 3511...

weak form of Hall's conjecture would follow from the ABC conjecture. A generalization to other perfect powers is Pillai's conjecture, though it is also...

together with Juliusz Brzeziński, he formulated the n-conjecture—a version of the abc conjecture involving n > 2 integers. "Zmarł Profesor Jerzy Browkin...

counterexample to the Bombieri–Lang conjecture and to the abc conjecture. It would also solve Harborth's conjecture, on the existence of drawings of planar...

follow from the abc conjecture that there are only finitely many Brown numbers. More generally, it would also follow from the abc conjecture that n ! + A =...

Diophantine geometry. With Joseph Oesterlé in 1985, Masser formulated the abc conjecture, which has been called "the most important unsolved problem in Diophantine...

investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the...

Granville and Stark showed that a certain uniform formulation of the abc conjecture for number fields implies "no Siegel zeros" for negative discriminants...

These approximations imply solutions to important problems like the abc conjecture. The extensions of F1 later on were denoted as Fq with q = 1n. Together...

its smallest term must be congruent to 7, 27, or 35 modulo 36. If the abc conjecture is true, there are only a finite number of sets of three consecutive...