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math helllllllllllpppp plzzzzzzzzzzzzzzzzzzzzzzz

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What are the last 2 digits of 43^2082?

  • math helllllllllllpppp plzzzzzzzzzzzzzzzzzzzzzzz - ,

    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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