Rational Points on Elliptic Curves pp 9-37 | Cite as

# Geometry and Arithmetic

Chapter

## Abstract

Everyone knows what a rational number is, a quotient of two integers. We call a point in the ( with

*x*,*y*) plane a*rational point*if both its coordinates are rational numbers. We call a line a*rational line*if the equation of the line can be written with rational numbers; that is, if its equation is$$ax + by + c = 0$$

*a*,*b*,*c*,rational. Now it is pretty obvious that if you have two rational points, the line through them is a rational line. And it is neither hard to guess nor hard to prove that if you have two rational lines, then the point where they intersect is a rational point. If you have two linear equations with rational numbers as coefficients and you solve them, you get rational numbers as answers.### Keywords

Sine Fermat sinO## Preview

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## Copyright information

© Springer Science+Business Media New York 1992