Pell's Equation Unlocked: From Ancient Puzzles to Modern Algorithms

Join us as we unravel Pell's equation, the ancient Diophantine treasure x^2 - n y^2 = 1. We’ll trace its history—from Brahmagupta and the Chakravala method to Archimedes’ cattle problem and the Fermat–Euler tale—and explain how continued fractions reveal fundamental solutions that generate infinitely many others. We’ll also peek into big-number solvers like the quadratic sieve and explore the twist of the negative Pell equation.

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