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

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- by Mao Hua Le
- Proc. Amer. Math. Soc.
**117**(1993), 1-3 - DOI: https://doi.org/10.1090/S0002-9939-1993-1110547-7
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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 $x_1^2 + \cdots + x_k^2 \equiv 0\;(\bmod p)$, $1 \leqslant {x_1} < \cdots < {x_k} \leqslant (p - 1)/2$.## References

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## Bibliographic Information

- © Copyright 1993 American Mathematical Society
- 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