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我们从一些智力竞赛题中不难发现,有些计算题或证明题是不能单从一般的演算,或由一、二个式子的推理就可解决的,而是要根据题目所提供的条件进行逻辑变换,合理分解,从而探索出其解题的技巧,最后求得题目所需要的答案或证明。现举二例如下: 例1 证明111~111+112~112+113~113能被10整除。本题如一个一个地乘方出来再求和来证明,恐怕费尽数小时也难以证出来的。因此,这类题的证明方法关键就是要注意一个“巧”字。请看下面的分析与证明:
We can easily find out from some quiz questions that some calculation questions or proving questions cannot be solved from the general calculus alone, or from the inference of one or two formulas, but based on the conditions provided by the questions. Logical transformation, reasonable decomposition, so as to explore the skills of solving problems, and finally find the answers or proofs needed for the topic. Here are two examples: Example 1 proves that 111~111+112~112+113~113 can be divisible by 10. If this question is proved one by one and then summed up to prove it, I am afraid it will be difficult to prove it after spending hours. Therefore, the key to the proof of such questions is to pay attention to a “smart” word. Please see the following analysis and proof: