Wednesday, February 23, 2011

Mirror numbers

Notice the following examples:

(1)

12^2 = 144 ........................ 21^2 = 441
13^2 = 169 ........................ 31^2 = 961

102^2 = 10404 ................. 201^2 = 40401
103^2 = 10609 ................. 301^2 = 90601
112^2 = 12544 ................. 211^2 = 44521
113^2 = 12769 ................. 311^2 = 96721

1012^2 = 1024144 ........... 2101^2 = 4414201
1112^2 = 1236544 ........... 2111^2 = 4456321
1212^2 = 1468944 ........... 2121^2 = 4498641
2012^2 = 4048144 ........... 2102^2 = 4418404



(2)


21^2 - 12^2 = 441 - 144 = 297
31^2 - 13^2 = 961 - 169 = 792



Could find other examples?


(3)

If x and y are mirror numbers and their product x * y = 53703
then x= 153 and y = 531

How do you go about it to find these two numbers?

Notice that

The factors of 53703 are:

1 3 9 13 17 27 39 51 81 117 153 221 243 351 459 663 1053 1377 1989 3159 4131
5967 17901 53703

The prime factors are: 3 * 3 * 3 * 3 * 3 * 13 * 17

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