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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1110547
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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$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1110547-7
PII: S 0002-9939(1993)1110547-7
Article copyright: © Copyright 1993 American Mathematical Society