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

• Nov 17th 2012, 11:30 AM
wilhelm
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.
• Nov 17th 2012, 12:22 PM
a tutor
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.