我在做竞赛题时体会到,一些对称的不定方程可以用极端的方法解决.这种方法很有代表性,为突出方法的重要性,例题都选自自主招生的真题.例1(2012年清华保送生考试)求不定方程1/x+1/y+1/z=1的所有正整数解(x,y,z).解不妨设x≤y≤z,由对称性,先令x=y=z,则x=3,于是只有:x=2或x=3,当x= In my quizzes, I realized that some symmetric indefinite equations can be solved in extreme ways.This method is very representative and in order to highlight the importance of the method, examples are chosen from the real questions of self-enrollment.Example 1 (2012 (X, y, z) for the undetermined equation 1 / x + 1 / y + 1 / z = 1. Let x = y ≤ z be the solution, and x = y = z, then x = 3, then only: x = 2 or x = 3, when x =