Elliptic Curves in Recreational Number Theory

TL;DR

This paper explores recreational mathematics problems linked to elliptic curves, emphasizing the challenge of finding rational points of large height that remain undiscovered, highlighting the intersection of number theory and recreational math.

Contribution

It introduces a collection of recreational problems connected to elliptic curves, emphasizing the difficulty of locating large-height rational points.

Findings

Many problems lead to searching for large-height rational points.

Such points have not yet been found for several problems.

The work connects recreational math with elliptic curve theory.

Abstract

Several problems which could be thought of as belonging to recreational mathematics are described. They are all such that solutions to the problem depend on finding rational points on elliptic curves. Many of the problems considered lead to the search for points of very large height on the curves, which (as yet) have not been found.