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贵刊1984年第二期所登出的《利用余数定理证一类整除性问题》一文中介绍的证题方法,简单明了,且文中所谈证法较之数学归纳法的证明显得更加易懂。但文中例4一题在证明过程中,三次用到余数定理,使证题过程过于冗长,这里仅用原文中的方法将例4的证明加以改进。例4 设n为自然数,试证6~(2n)+3~(n+2)+3~n能被11整除。证∵6~(2n)+3~(n+2)+3~n=12~n·3~n+10·3~n
The testimony method described in the article “Using the remainder of theorem certificate” in the second issue of the magazine published in 1984 is simple and clear, and the proof in the text seems to be more understandable . However, in the proof process of Example 4, the remainder theorem is used three times to make the process of the proof excessively lengthy. Here, the proof of Example 4 is only improved by the original method. Example 4 Let n be a natural number and testify that 6~(2n)+3~(n+2)+3~n can be divisible by eleven. ∵6~(2n)+3~(n+2)+3~n=12~n•3~n+10•3~n