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Last digit, mod 8

  1. Aug 14, 2010 #1
    1. The problem statement, all variables and given/known data
    What is the last digit of 101000 (mod 8)

    2. Relevant equations

    3. The attempt at a solution

    10^2[tex]\equiv[/tex]4 (mod 8)

    (10^2)^500[tex]\equiv[/tex] 4^500 (mod 8)

    4^2=0 (mod 8)

    (4^2)^250[tex]\equiv[/tex]0^250[tex]\equiv[/tex]0 (mod 8)

    Thus, the last digit is 0.

    Are these steps mathematically legal?
    Last edited: Aug 14, 2010
  2. jcsd
  3. Aug 15, 2010 #2
    ya, what you have done is absolutely fine
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