Posted by **jamesbond** on Tuesday, May 14, 2013 at 2:16pm.

What are the last 2 digits of 43^2082?

- math helllllllllllpppp plzzzzzzzzzzzzzzzzzzzzzzz -
**Reiny**, Tuesday, May 14, 2013 at 3:35pm
43^0 = 1 or 01

43^1 = 43

43^2 = 1849

43^3 = 79507

43^4 = 3418801

43^5 = 147008443

43^6 = ......049

43^7 = ..... 07

43^8 = ..... 01

43^9 = ..... 43

ahhh, can you see how the end repeats ?

ending: 43 49 07 01 43 repeats after 4 numbers

2082/4 = 520 and remainder of 1

and behaves like

43^1 , 1/4 = 0 and a remainder of 1 ---ends in 43

43^9, 9/4 = 2 and a remainder of 1 --- ends in 43

..

43^2082 , 2082/4 = 520 and a remainder of 1 --- ends in 43

So 43^2082 ends in a 43

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