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The Equation $x^2+\overline m y^2=\overline k$ in ℤ/p

Kurt Girstmair
The American Mathematical Monthly
Vol. 120, No. 6 (June–July 2013), pp. 546-552
DOI: 10.4169/amer.math.monthly.120.06.546
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Page Count: 7
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Item Type
The Equation 

$x^2+\overline m y^2=\overline k$

 in ℤ/pℤ
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Abstract We present a simple and character-free approach to the determination of the number of nontrivial solutions of the equation \documentclass{article} \pagestyle{empty}\begin{document} $x^2+\overline m y^2=\overline k$ \end{document} in ℤ/pℤ, where m and k are integers not divisible by p.

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