Question

What are the last 2 digits of 43^2082?

Answer 1

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