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Math Help - What is the units digit of the following number (sum of powers)

  1. #1
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    What is the units digit of the following number (sum of powers)

    Hello.

    I'm having problems solving this problem. What is the units digit of the following number:

    (1- \sqrt{3} )^{2000} + (1+ \sqrt{3} ) ^{2000}

    I wouldn't have any problems solving this, were it not for the square root of 3. Please, help.
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  2. #2
    Senior Member
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    Re: What is the units digit of the following number (sum of powers)

    u_{n+2}=u_{n+1}+u_n, n\ge 1

    u_1=2, u_2=8

    Maybe there's a better way but looking at this sequence and taking remainders on division by 10 we get 2,8,0,6,2,6,6,4,etc..

    Perhaps I'll say more later.
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