How to Solve a Diophantine Equation

TL;DR

This paper introduces Diophantine equations, discusses their complexity, and demonstrates solving a specific equation related to Pascal's Triangle using advanced methods.

Contribution

It provides an accessible introduction to Diophantine equations and showcases a modern approach to solving a particular challenging example.

Findings

Diophantine equations can be computationally hard to solve.

A specific Pascal's Triangle related equation was successfully solved.

The paper illustrates the application of advanced solution techniques.

Abstract

These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one can solve a specific equation related to numbers occurring several times in Pascal's Triangle with state-of-the-art methods.