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Last 4 digits of a^1000?

  1. Feb 14, 2008 #1
    1. The problem statement, all variables and given/known data

    for 2<= a <=10
    what is the last 4 digits of a^1000?
    What is the criterion for the prediction of the last 4 digits from a?
     
  2. jcsd
  3. Feb 14, 2008 #2
    i am not sure
    but it looks like a tailor series with calculating and error
     
  4. Feb 14, 2008 #3

    malawi_glenn

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    use modulus when you divide a^1000 with 10000 ?
     
  5. Feb 14, 2008 #4
    would there be a formula?
     
  6. Feb 14, 2008 #5

    malawi_glenn

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    you dont know how modulus work?
     
  7. Feb 14, 2008 #6
    Try using modulus and Euler's Theorem (if you're dealing with the prime a). Or you could try finding the order of a mod 10000 and using modulo arithmetic from there. That should reduce the problem to a much simpler one - at least, you won't have to multiply a out 1000 times.
     
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