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问题及解答

完全平方数的特征

Posted by haifeng on 2016-04-03 15:12:02 last update 2016-04-03 15:28:57 | Edit | Answers (0)

完全平方数指一个整数的平方. 

如 0,1,2,3,...,99 的平方是

 

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289,
324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 
1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 
2116, 2209, 2304, 2401, 2500, 2601, 2704, 2809, 2916, 3025, 3136, 3249, 3364, 
3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356, 4489, 4624, 4761, 4900, 5041, 
5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 
7225, 7396, 7569, 7744, 7921, 8100, 8281, 8464, 8649, 8836, 9025, 9216, 9409, 
9604, 9801

 

其末尾数字只可能取下面的值: 0, 1, 4, 9, 6, 5.

我们注意到上面这些数末尾数字的变化规律是 0, 1, 4, 9, 6, 5; 6, 9, 4, 1, 0, 1, 4, 9, 6, 5, ... . 即

0, 1, 4, 9, 6, 5;

------- > ------
_______________|
|_______________

 

 

请证明这个规律.