Pell Equation

Pell Equation

Pell's Equation

For non-square D, x² - Dy² = 1 always has infinite solutions. The fundamental solution (x, y) generates all others via (x + y√D)ⁿ.

Example: D=2 → 3² − 2×2² = 9 − 8 = 1 ✓

Algorithm

Continued fraction convergents of √D. Precomputed D ≤ 10,000 + Cattle; others on-the-fly.