用讨论的方法求出整数解

• 作 者: 张肇平 吴佳薇
• 出 处: 数学大世界(初中版)
• 发表日期: 2013年04期
• 关键词: 方法 整数解 具体的做法 分类讨论 不定方程 奇偶数 竞赛中 运用 数学 分式

在数学竞赛中有许多涉及整数解的问题,有些问题要根据整数的性质,用分类讨论的办法,探究各种情况,最后求得结论.具体的做法有归结为不定方程的整数解,归结为积或分式讨论约数,或分奇偶数讨论或罗列各种情况一一列出,下面以近年来的赛题为例,探讨这一方法的运用.一、归结为积或商,讨论约数例1已知正整数a,b的最大公约数是3,最小公

There are many problems involved in integer solution in mathematical contest, some questions should be based on the nature of integers, using the method of class discussion to explore various situations, and finally to draw conclusions .Specific approach boils down to the integer solution of the indefinite equation, boiled down to Product or fractional discussion of divisor, or sub-odd or even discuss the various situations listed one by one, the following questions in recent years, for example, to explore the use of this method. Example 1 Known as a positive integer a, b the greatest common divisor is 3, the smallest male