🔬 BTYSTE 2020
done
A mathematical project which describes a elegant and simple iterative method for generating solutions to Diophantine equations, given a single initial solution.
I worked on this project for a couple months when I was 12 and presented it at:
- BT Young Scientist and Technology Exhibition 2020 (🥉 3rd Place) • Dublin, Ireland
Project Abstract
A Simple Iterative Method for Solving Diophantine Equations
By Aditya Joshi
A Diophantine equation is one that must be solved using only integers. In 1900 David Hilbert asked if there was any one method that would solve all Diophantine equations (Hilbert's Tenth Problem).
In 1970 Yuri Matiyasevich proved that no such method exists. Equations that seem very similar may require very different methods of solution.
This project describes a method whereby, for certain Diophantine equations, a sequence of solutions can be generated from one known solution. This method requires only very simple algebra. Computer algorithms that implement the method further increase its effectiveness.