A Necessary and Sufficient Condition for Existence of a Rational Point on an Elliptic Curve
Abstract
In this paper, the proof of the existence of a rational point on an elliptic curve is transformed into the proof of the existence of an integer solution for a Diophantine equation. By a new formula for calculating the number of elements in intersection of two finite sets, a necessary and sufficient condition for existence of a rational point on an elliptic curve is established. This condition is different from L-function in the Birch and Swinnerton-Dyer conjecture.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.