论文标题
与物业的二元三元二元组成$ d（n）$不同的$ n $
Diophantine triples with the property $D(n)$ for distinct $n$
论文作者
论文摘要
我们证明，对于每个整数$ n $，都存在无限的$ d（n）$ - 三倍，也是$ d（t）$ - $ t \ in \ mathbb {z} $带有$ n \ ne t $的$ t \。我们还证明，属性$ d（-1）$ in $ \ mathbb {z} [i] $也有无限的三倍，它也是$ d（n）$ - 三重$ \ mathbb {z} [z} [i] $，对于两个$ n $ n = -1 $以外的$ n = -1 $，这些三倍与这些$ ncorpive $ n均与$ d（$ n均与$ diple）相等。
We prove that for every integer $n$, there exist infinitely many $D(n)$-triples which are also $D(t)$-triples for $t\in\mathbb{Z}$ with $n\ne t$. We also prove that there are infinitely many triples with the property $D(-1)$ in $\mathbb{Z}[i]$ which are also $D(n)$-triple in $\mathbb{Z}[i]$ for two distinct $n$'s other than $n = -1$ and these triples are not equivalent to any triple with the property $D(1)$.
