Proof of Divisibility of 8 rule

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Homework Statement


Let n be a natural number. If the number formed by the last three digits of n is divisible by 8, then n is divisible by 8.


Homework Equations


Natural numbers are the set of {1,2,3,4,5,6,...}


The Attempt at a Solution


I believe we should use a direct proof to prove this conditional statement. Thus we will assume that n is a natural number and the number formed by the last three digits of n is divisible by 8. We will prove that n is divisible by 8.
I don't know where to go from here. Please help!
 
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Hint: What is the lowest power of 10 that is divisible by 8?
 
Reply to Hint

Okay so 1000 is the lowest power of 10 that is divisible by 8. How do I use that?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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