Permutations of Subscripts for Unchanged Value in Polynomial Symmetry

polarbears
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Homework Statement


(x_1 - x_2)(x_3 - x_4)
Find permutations of subscripts that leave value unchanged

Homework Equations


The Attempt at a Solution


Okay so I know that it's asking how I should rearrange things and still not change the value.
Switching 1 with 2 or 3 with 4 would work but I know there's more than that but I'm don't know how to show it.
I guess I can expand it but I'm not sure if that helps
 
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"Switching 1 with 2 OR 3 with 4" doesn't work, "switching 1 with 2 AND 3 with 4" does. How about switching 1 with 3 and 2 with 4? Hmm?
 

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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