By an oval in \({\mathbb {Z}}^2_{2p},\)p odd prime, we mean a set of \(2p+2\) points, such that no three of them are on a line. It is shown that ovals in \({\mathbb {Z}}^2_{2p}\) only exist for \(p=3,5\) and they are unique up to an isomorphism.

中文翻译：

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$$ {\ mathbb {Z}} ^ 2_ {2p} $$ Z 2 p 2的椭圆形

通过\（{\ mathbb {Z}} ^ 2_ {2p}，\）p奇数质的椭圆，我们表示一组\（2p + 2 \）点，使得它们中没有三个在一条线上。结果表明，\（{\ mathbb {Z}} ^ 2_ {2p} \）中的椭圆仅对于\（p = 3,5 \）存在，并且直到同构为止都是唯一的。