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Homework Help: Calculate 2^100 in ZZ11?

  1. May 14, 2017 #1
    1. The problem statement, all variables and given/known data
    Calculate 2^100 in ZZ11.

    2. Relevant equations
    This is a Linear Algebra problem.

    3. The attempt at a solution
    Here's my work:
    2^5=32=-1 mod 11
    2^10=1 mod 11
    2^100=1 mod 11
    I think the answer is 1 since that's the remainder, am I right?
  2. jcsd
  3. May 14, 2017 #2
    You are correct. Note also that 2^10 = 1024 = 93*11 + 1.
  4. May 14, 2017 #3


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    Staff Emeritus
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    I gather that you are referring to ℤ11 .

    In trying to see if ZZ was the same as ℤ, I came across the following link:
    Here is a screen shot of the page that link takes you to.

    Is that a coincidence ?
  5. May 16, 2017 #4


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    Staff: Mentor

    It's generally okay if they are posting in a couple of places looking for help. As long as they don't post links to the other forums here. :smile:
  6. May 16, 2017 #5


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    Staff: Mentor

    If you are just interested in checking the answer, WolframAlpha can do that - the answer is 1.
  7. May 16, 2017 #6


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    I think it would only be polite if a good solution given in one forum were put into the other threads. But that presents other issues.
  8. May 18, 2017 #7
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