Z^4中的等边三角形
Equilateral triangles in Z^4
摘要：
我们给出了所有三个点在$\mathbb R^4$与整数坐标是在相同的欧氏距离的表征。在三维空间中，问题的特征在于丢番图方程$a^2+b^2+c^2=3d^2$的解决方案。在$\mathbb R^4$中，表征基本上基于同一方程的两个不同解。
英文摘要：
We give a characterization of all three points in $\mathbb R^4$ with integer coordinates which are at the same Euclidean distance apart. In three dimension the problem is characterized in terms of solutions of the Diophantine equations $a^2+b^2+c^2=3d^2$. In $\mathbb R^4$, the characterization is essentially based on two different solutions of the same equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
