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Let $p=4k+1$ be a prime number such that $p=a^2+b^2$, where $a$ is an odd integer.Prove that the equation $x^2-py^2=a$ has at least a solution in $\mathbb{Z}$.

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    @GerryMyerson, Ah, in my defence, that wasn't made very clear.2012-08-06

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See e.g. Gary Walsh, On a question of Kaplansky".

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    Abstract here: http://mr.math.ca/Vol_23/No_2.html2012-08-07