论文标题
$ k $ -dioophantine $ m $ - 有限字段
$k$-Diophantine $m$-tuples in Finite Fields
论文作者
论文摘要
在本文中，我们将$ k $ -dioophantine $ m $ $ tuple定义为一组$ m $阳性整数，以使任何$ k $ distion的正整数的产品比一个完美的广场少一个。我们在有限字段中研究这些集合$ \ mathbb {f} _p $ for Odd Prime $ p $，并保证存在$ k $ -dioophantine m-tuple提供$ p $的$ P $大于某些明确的下限。我们还提供了$ \ mathbb {f} _p $的3-二磷酸三元组的公式，以及$ k $ -dioophantine $ k $ tuples的渐近公式。
In this paper, we define a $k$-Diophantine $m$-tuple to be a set of $m$ positive integers such that the product of any $k$ distinct positive integers is one less than a perfect square. We study these sets in finite fields $\mathbb{F}_p$ for odd prime $p$ and guarantee the existence of a $k$-Diophantine m-tuple provided $p$ is larger than some explicit lower bound. We also give a formula for the number of 3-Diophantine triples in $\mathbb{F}_p$ as well as an asymptotic formula for the number of $k$-Diophantine $k$-tuples.
