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29 April, 14:35

What is the remainder of 10^2017 divided by 1001?

This probably incorporates some number theory, which I'm not good at. RIP

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  1. 29 April, 15:00
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    Note: When I use the double equal sign, I mean the triple bar used with modular arithmetic

    10^3 = 1000 = = - 1 (mod 1001)

    10^3 = = - 1 (mod 1001)

    (10^3) ^672 = = (-1) ^672 (mod 1001)

    (10^ (3*672) = = 1 (mod 1001)

    10^2016 = = 1 (mod 1001)

    10*10^2016 = = 10*1 (mod 1001)

    10^2017 = = 10 (mod 1001)

    Final Answer: 10
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