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The number of solutions of a certain quadratic congruence related to the class number of $ {\bf Q}(\sqrt{p})$


Author: Mao Hua Le
Journal: Proc. Amer. Math. Soc. 117 (1993), 1-3
MSC: Primary 11D79; Secondary 11R11, 11R29
DOI: https://doi.org/10.1090/S0002-9939-1993-1110547-7
MathSciNet review: 1110547
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ p$ be an odd prime, and let $ k$ be a positive integer with $ i \leqslant k \leqslant (p - 1)/2$. In this note we give a formula for the number of solutions $ ({x_1}, \ldots ,{x_k})$ of the congruence $ x_1^2 + \cdots + x_k^2 \equiv 0\;(\bmod p)$, $ 1 \leqslant {x_1} < \cdots < {x_k} \leqslant (p - 1)/2$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1110547-7
Article copyright: © Copyright 1993 American Mathematical Society