Pell Equation Calculator

Find solutions to Pell's equation x² - Dy² = 1 using continued fractions.

Pell Equation Parameters

D (non-square positive integer)

Number of Solutions

Pell's equation has infinitely many solutions when D is not a perfect square.

x² - Dy² = 1

All solutions can be generated from the fundamental solution (x₁, y₁).

xₙ₊₁ = x₁xₙ + Dy₁yₙ

yₙ₊₁ = x₁yₙ + y₁xₙ

Equation

x² - 2y² = 1

x₁

y₁

n = 1Valid

x = 3

y = 2

n = 2Valid

x = 17

y = 12

n = 3Valid

x = 99

y = 70

n = 4Valid

x = 577

y = 408

n = 5Valid

x = 3363

y = 2378

n = 6Valid

x = 19601

y = 13860

n = 7Valid

x = 114243

y = 80782

n = 8Valid

x = 665857

y = 470832

n = 9Valid

x = 3880899

y = 2744210

n = 10Valid

x = 22619537

y = 15994428