How Many Ring Homomorphisms Exist from Z to Z?

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Homework Statement


number of ring homomorphisms from Z \rightarrow Z?


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The Attempt at a Solution


According to this information on ring homo, There is no ring homomorphism Zn → Z for n > 1. But I guess that doesn't hold for when n = 1, any ideas
 
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Any homomorphism must map identities to identities so a ring homomorphism must map 0 to 0 and 1 to 1. Now, any positive integer, n, can be written as a sum of "1"s. Therefore?
 
Awesome, I figured it out, thanks
 

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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