Explore: Mordell Conjecture

This was conjectured in 1922 by Louis Mordell, and known as the Mordell conjecture until its 1983 proof by Gerd Faltings. The conjecture was later generalized

101, 103, 131, 149, 157, 233, 257 and 263. In the 1920s, Louis Mordell posed a conjecture that implied that Fermat's equation has at most a finite number

of numbers. His basic work on Mordell's theorem is from 1921 to 1922, as is the formulation of the Mordell conjecture. He was an Invited Speaker of the

functions, is a special application but capable of proving cases of the Mordell conjecture for curves whose Jacobian's rank is less than its dimension. It developed

The Mordell conjecture (already proven in general by Gerd Faltings). As equivalent, Vojta's conjecture in dimension 1. The Erdős–Woods conjecture allowing

conjecture for abelian varieties over number fields, the Shafarevich conjecture for abelian varieties over number fields and the Mordell conjecture,

OEIS: A103953 for the smallest solution (> 0). Beal's conjecture Equation xy = yx Fermat–Catalan conjecture Mordell curve Ramanujan–Nagell equation Størmer's theorem

mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to

Faltings's solution of the Mordell conjecture. Zarhin extended these results to any finitely generated base field. The Tate conjecture for divisors on abelian

the method of Mordell's proof of the first two conjectures for holomorphic cusp forms. The more general Ramanujan–Petersson conjecture for holomorphic