The last digit is interesting

1^3 = 1  ...The last digit is 1

2^3 = 8  ...The last digit is 8

3^3 = 27  ...The last digit is 7

4^3 = 64  ...The last digit is 4

5^3 = 125  ...The last digit is 5

6^3 = 216  ...The last digit is 6

7^3 = 343  ...The last digit is 3

8^3 =512  ...The last digit is 2

9^3 = 9  ...The last digit is 1

1^3 + 2^3 + 3^3 ... + 2009 ^3...The last digit is ?

http://mypaper.pchome.com.tw/littleflea/post/1320358530

(撲朔迷您 11 :解答 961 =31^2, 961 + 888 = 1849 = 43^2

用平方差公式
A=N^2 ,B=M^2

A+111=B
=>B-A=111=37*3
=>(M+N) (M-N)=37*3
M=20 ,N=17
289+111=20^2

A+33=B
=>B-A=33=11*3
=>(M+N) (M-N)=11*3
M=7 ,N=4
16+33=7^2