Does every soluble negative pell equation, $a^2-Db^2=-1$, have infinitely many integer solutions $(a,b)$ where $a,b$ are both positive integers?
2026-04-07 06:09:44.1775542184
Question about Negative Pell Equations
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Assume that $D$ is an integer greater than $1$. From a solution $(a,b)$ of the equation $a^2-Db^2=-1$, we can obtain infinitely many solutions $(a_n,b_n)$ by setting $$a_n+b_n\sqrt{D}=(a+b\sqrt{D})^{2n+1}.$$