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形如3x+2y=15或2x+3y+7z=100之类的方程,其解是无数的,并且就是连非负整数解也有多种可能,因此求解起来较难,下面本人介绍两种求不定方程非负整数的解法.引例求28a+30b+31c=365的非负整数解.方法一:放缩法分析通过放大和缩小方程左边,从而得到a+b+c的一个取值范围而完成解题.解:由28(a+b+c)≤28a+30b+31c=365,得a+b+c≤365/25<13.04,所以a+b+c≤13.由31(a+b+c)≥28a+30b+31c=365,得a+b+c≥365/31>1 1.7,所以a+b+c≥12,于是有a
For equations such as 3x+2y=15 or 2x+3y+7z=100, the solution is innumerable, and there are also many possibilities for even non-negative integer solutions. Therefore, it is difficult to solve the equation. I will introduce two kinds of solutions. The non-negative integer solution of the indefinite equation. The cited example seeks the non-negative integer solution of 28a+30b+31c=365. Method One: The scalar law analysis enlarges and reduces the left side of the equation to obtain a range of values for a+b+c. Solve the problem. Solution: From 28 (a + b + c) ≤ 28a + 30b + 31c = 365, get a + b + c ≤ 365/25 <13.04, so a + b + c ≤ 13. By 31 (a + b + c) ≥ 28a + 30b + 31c = 365, get a + b + c ≥ 365/31> 1 1.7, so a + b + c ≥ 12, so there is a