Euclid's Algorithm Homework: Stuck & Need Help

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Look at 5 and 7. I cleverly observe that 3*5-2*7=1. Now any integer is a multiple of 1, right?
 
yeah...
 
...go on...
 
So n=(3*n)*5+(-2*n)*7. Doesn't that look like a linear combination of 5 and 7?
 
:)

great - thanks - i have got all the others now.
 

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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