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Math 324 homework help Alberta university

Question - Math 324 Assignment 5 (due October 15) 1.(6) Consider the sum ∑ ω ω k, where ω varies over all n complex roots of x n − 1. Show that this sum equals n if n di vides k, and equals 0 otherwise. 2.(6) Show that the greatest common divisor of 4k + 6 and 6k + 7 is 1, for all integers k. 3.(5) (9.1, #12) Let a, b, and m ≥ 1 be integers with a, b both relatively prime to m. Show that ord m(ab) = ordm(a)⋅ordm(b) if ordm(a) and ordm(b) are relatively prime. 4.( 2+2+2 ) Determine all primitive roots mod p, when p = 11, 13, and 17. 5.( 5) Suppose that r and s are both primitive roots mod m. Show that indr(a) ≡ indr(s) ⋅inds(a) mod φ(m) holds for all a with (a, m) = 1. 6.( 6) (9.4, #4) Dete ...Read More

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