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Diophantine approximation

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For a nonsquare positive integer $D$, the Pell equation is
$$
x^2-Dy^2=1.
$$
Periodic <continued fraction>[continued fractions] of $\sqrt D$ produce infinitely many integer solutions.

Pell equation

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 4 / 1G / Solution

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Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 20G / Solution

Pell equation

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Pell equation

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