一个三角不定方程的机器解法

AUTOMATED SOLVING METHODS FOR A TRIGONOMETRIC INDETERMINATE EQUATION

研究了如下具有几何意义的三角不定方程(采用角度制)sin(x°)sin(y°)sin(z°)/sin(A°-x°)sin(B°-y°)sin(C°-z°)=1其中A,B,C是给定的正整数,满足2≤A≤B≤C且A+B+C=180;1≤x≤A-1,1≤y≤B-1,1≤x≤C-1.设计了两种求解方案,使用计算机按两种求解方案完整的求出了上述方程的所有正整数解.

This paper studies the following trigonometric indeterminate equation with geometric significance （using degree measure） where A,B,C are given positive integers satisfying 2 ≤ A≤ B≤ C,A＋B＋C -- 180, 1 ≤ x ≤ A- 1, 1 ≤ y ≤ B-1, 1 ≤ z ≤C- 1. Two methods to the above equation are formulated. Following these two methods, all positive integer solutions of the equation are obtained via computer.