Prove the following identity

the sum running through and the matrix being of size .

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#
linear algebra

# [Some punny title about determinants and fixed points]

# Its hip to be skew

# The order of an automorphism

# Keeping it real

# A generic curve

# Polynomial Decomposition

# Sum of powers

Prove the following identity

the sum running through and the matrix being of size .

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Show that the determinant of a skew symmetric matrix is never reducible when viewed as a polynomial in variables.

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.

Provide the most elegant proof to the following claim you can produce. Suppose and are nonzero complex numbers and for every positive integer it is true that . then and the are a reordering of the .