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Replace p by q in this problem where q is a prime power and


The trace mapping Tr is defined on GF(p), p prime, by

1679_301cf1b2-883c-4a23-9b13-7cdf4819cf2e.png

a) Prove that Tr (x) GF (p), for every

1679_301cf1b2-883c-4a23-9b13-7cdf4819cf2e.png

b) Prove that Tr is a linear mapping (hint: Cor. B.28).

c) Prove that Tr takes on every value in GF(p) equally often.

d) Replace p by q in this problem, where q is a prime power, and verify the same statements.

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Chemical Engineering: Replace p by q in this problem where q is a prime power and
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