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猜想：整数等差数列的性质

2008-12-21 01:20:11| 分类：猜想 | 标签： |举报 |字号大中小订阅

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   朋友们，我又发现了有些东西。就是——整数等差数列{An}连续四项的平方和必能被3整除。（公差不为3的整数倍）
   即
   当An=An+B，(A∈Z且A≠3，B∈Z)时，若x=（An）^2+（An+1）^2+（An+2）^2+（An+3）^2，（n∈Z+），
   则x能被3整除。
   同样是那句话——希望有人能给出完整的证明，或找出一个反例来否定它。

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