论文标题
与佩尔方程的角度双压和解有关的双方方程
Diophantine equation related to angle bisectors and solutions of Pell's equations
论文作者
论文摘要
在绘制技术中，要找到两条直线及其角度的两种斜坡的组合非常重要。该问题减少为解决diophantine方程$（a-c）^2（b^2+1）=（b-c）^2（a^2+1）。$在本文中，我们描述了该方程的所有非平凡积分解决方案，并具有负Pell方程的解决方案。该公式通过佩尔方程解决方案的某些属性（例如半企业佩尔数和佩尔数字）的某些属性证明。我们还提供了一个公式，该公式由毕达哥拉斯的三元组产生的合理解决方案，腿部相同。
It is important in drawing techniques to find combinations of two straight lines and their angle bisectors whose slopes are all rational numbers. This problem is reduced to solving the Diophantine equation $(a-c)^2(b^2+1) = (b-c)^2(a^2+1).$ In this article, we describe all nontrivial integral solutions of the equation with solutions of negative Pell's equations. The formula is proven by certain properties of solutions of Pell's equations like those of half-companion Pell numbers and Pell numbers. We also give a formula for its rational solutions produced by Pythagorean triples with identical legs.
