Math

Find the last two digits of the number 11^2016 .

I need to figure out how to hand do this and show all my work. Help pls

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  1. Start a table of the powers of 11
    n 11^n
    1 11
    2 121
    3 1331
    4 14641

    The last 2 digits just cycle through
    11
    21
    31
    ...
    91
    01
    11
    21
    ...
    So, 11^2016 ends in 61

    Or, you might find this article on modular arithmetic useful:

    https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/fast-modular-exponentiation

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