完全平方数的特征
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;
------- > ------
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请证明这个规律.