论文标题
假想二次场中的某些双苯胺元素
Certain Diophantine Tuples in Imaginary Quadratic Fields
论文作者
论文摘要
令$ k $为一个虚构的二次字段，$ \ mathcal {o} _k $是其整数环。 a集$ \ {a_1，a_2，\ cdot，a_m \} \ subset \ mathcal {o} _k \ setMinus \ {0 \} $称为diophantine $ m $ m $ -tuple，in $ \ nathcal {o} x_ {ij}^2 $，其中$ x_ {ij} \ in \ mathcal {o} _k $ for All $ i，j $，因此$ 1 \ leq i <j \ j \ leq m $。在这里，我们证明了$ \ Mathcal {o} _k $的diophantine $ m $ tuples的不存在，$ d（-1）$ for $ m> 36 $。
Let $K$ be an imaginary quadratic field and $ \mathcal{O}_K$ be its ring of integers. A set $\{a_1, a_2, \cdots,a_m\} \subset \mathcal{O}_K\setminus\{0\}$ is called a Diophantine $m$-tuple in $\mathcal{O}_K$ with $D(-1)$ if $a_ia_j -1 = x_{ij}^2$, where $x_{ij} \in \mathcal{O}_K$ for all $i,j$ such that $1 \leq i < j \leq m$. Here we prove the non-existence of Diophantine $m$-tuples in $\mathcal{O}_K$ with $D(-1)$ for $m > 36$.
