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Sep 15, 2015 at 23:58 vote accept unknown
Sep 10, 2015 at 19:40 comment added unknown Thanks for the response. The motivation for the question came from a totally different angle (optics); I didn't think of the problem in terms of factoring. If I follow your answer correctly this would imply that adding the requirement that the matrix is invertable would mean that only the case $n=2$ has solutions. This negative result would have value on its own. Do you have a good reference for the irreducibality of the fermat curve? also the fermat curve is in only 3 variables, can I assume that the general $\sum_1^n x_i^n$ is also irreducible?
Sep 10, 2015 at 1:10 history answered Alexander Smith CC BY-SA 3.0