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.