hw10 - p416, E8(iii) No, because this polynomial is...

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MATH 3360 HOMEWORK SOLUTION 10 (Some computational problems are omitted.) p311, E3 (1 , 2 , 1 , 4) p311, E9 This is by the fact that b p - 1 = 1 but b ( p - 1) / 2 6 = 1. Handout In Lemma 1, you need ( ab ) mn = a mn b mn . This requires commutativity. Note that abstract Fermat Theorem also works for nonabelian groups.
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Unformatted text preview: p416, E8(iii) No, because this polynomial is divisible by x + 1. p418, E13 Note that x 2 + 1 has a root: let be a primitive element, then ( p-1) / 4 is a root of x 2 + 1 = 0. 1...
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