The Bogomolov-Miyaoka-Yau inequality implies the truth of this statement, as does a statement relating the minimal discriminant to a conductor of a certain type of curve called Szpiro's conjecture.
The Bogomolov-Miyaoka-Yau inequality implies the truth of this statement, as does a statement relating the minimal discriminant to a conductor of a certain type of curve called Szpiro's conjecture. One statement that leads to the proof of this statement is part of the Langlands program. The proof by Ken Ribet of the "epsilon conjecture," which stated that the Frey curve was not modular, led to a proof of a special case of the Taniyama-Shimura conjecture, whose truth implies the truth of this theorem. For ten points, identify this theorem which states that the equation "x to the n plus y to the n equals z to the n" has no nonzero integer solutions for integer n greater than two, eventually proved by Andrew Wile.
The Bogomolov-Miyaoka-Yau inequality implies the truth of this statement, as does a statement relating the minimal discriminant to a conductor of a certain type of curve called Szpiro's conjecture.
Fermat's Last Theorem