论文标题
二次场中某些二氧甘氨酸方程的积分解决方案
Integral solutions of certain Diophantine equation in quadratic fields
论文作者
论文摘要
令$ k = \ mathbf {q}（\ sqrt {d}）$为二次字段，$ \ mathcal {o} _ {k} $是其整数环。我们研究了diophantine方程$ r + s + t = rst = 2 $ in $ \ mathcal {o} _ {k} $。我们证明，除了$ d = -7，-1、17 $和$ 101 $之外，该系统在其他二次字段的整数中无法解决。
Let $K= \mathbf{Q}(\sqrt{d})$ be a quadratic field and $\mathcal{O}_{K}$ be its ring of integers. We study the solvability of the Diophantine equation $r + s + t = rst = 2$ in $\mathcal{O}_{K}$. We prove that except for $d= -7, -1, 17$ and $101$ this system is not solvable in the ring of integers of other quadratic fields.
