Finding 8 Numbers with phi(n) = 240

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Find eight different numbers n with phi(n) = 240.



phi(n) = the number of positive integers less than or equal to n, that are relatively prime to n.
 
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Surely you are aware that you must show what you have tried yourself before anyone can give suggestions?
 
12^12 = (3^12)(2^24)

phi(12^12) = phi(3^12) * phi(2^24) = 2^(24-1) * (2-1) *3^12 *(3-1)
= 2^23 * 3^12 * 2 = 2^24 * 3^12
 

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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