# Questions tagged [pell-type-equations]

Questions on finding integer solutions to bivariate equations of the form $x^2-Dy^2=a$.

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### Pell-Type Equation: show that the solutions $x,y$ are such that $\frac{x}{y}$ is a convergent

Prove that for any solution of the equation $x^2 − 14y^2 = 2$, in positive integers $x, y$ the value $\frac{x}{y}$ is a convergent of $\sqrt{14}$ I am not too sure where to start, I have the continued ...
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### Binary quadratic forms over Z of discriminant D [closed]

For each of the following 3 discriminant D = 4d, how can I classify all binary quadratic forms over Z of discriminant D. Is there a way to describe the river corresponding to the canonical form Q(x, y)...
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### fundamental solution of Pell’s equation under special conditions

I make the following conjecture from an answer. conjecture Suppose $N$ could be expressed as $$N= p^2\pm q,\ \ \ \ (p,q \in \mathbb{N},\ 1 \lt q \lt p,\ q\mid 2p)$$ In this case, the fundamental ...
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