Independent research · Ongoing

Pell's equation and quadratic Diophantine equations

Proof-based research, alongside Euler Circle and Stanford ULO coursework

I am investigating quadratic Diophantine equations, modular arithmetic, and Pell's equations through proof-based analysis. The question behind it is simple to state: when does an equation like x squared minus D times y squared equal 1 have whole-number solutions, and how can they all be found? It is the pure-mathematics side of my work, and it grew out of my proof-based coursework in Mathematical Thinking and Modern Algebra.

From Nov 2025ongoing investigation

Methods

Proof-Based Analysis
Modular Arithmetic
Pell's Equations
Number Theory

Try it

Find the smallest whole-number solution of x² − D·y² = 1D

x1766319049

y226153980

For D = 61 the smallest solution is already ten digits long. This is a general demonstration of Pell's equation, not a result from my research. It uses continued fractions, the classical method.

Connected work

University courses and PACT proofs, algebra

Next: Guha Lab, The University of Chicago →