In this paper, we study how small a box contains at least two points from amodular hyperbola $x y \equiv c \pmod p$. There are two such points in a squareof side length $p^{1/4 + \epsilon}$. Furthermore, it turns out that eitherthere are two such points in a square of side length $p^{1/6 + \epsilon}$ orthe least quadratic nonresidue is less than $p^{1/(6 \sqrt{e}) + \epsilon}$.
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机译：在本文中，我们研究了一个小盒子至少包含来自模块化双曲线$ x y \ equiv c \ pmod p $的两个点。在边长的平方$ p ^ {1/4 + \ epsilon} $中有两个这样的点。此外，事实证明，在边长为$ p ^ {1/6 + \ epsilon} $的正方形中有两个这样的点，或者最小二次非残差小于$ p ^ {1 /（6 \ sqrt {e}） + \ epsilon} $。
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