7. (a) Let p be prime. Suppose a and b are integers such that ab = 0 (mod p). Show that either a = 0 or b = 0 (mod p). (b) Show that if a, 6, n are integers with nlab and gcd(a, n) = 1, then n|b. 8. Let p 2 3 be prime. Show that the only solutions to 1' = 1 (mod p) are I = ±1 (mod p). (Hint: Apply Exercise 7(a) to (z+ 1)(1 - 1).)

7. (a) Let p be prime. Suppose a and b are integers such that ab = 0 (mod p). Show that either a = 0 or b = 0 (mod p). (b) Show that if a, 6, n are integers with nlab and gcd(a, n) = 1, then n|b. 8. Let p 2 3 be prime. Show that the only solutions to 1' = 1 (mod p) are I = ±1 (mod p). (Hint: Apply Exercise 7(a) to (z+ 1)(1 - 1).)

Name: please do 8 7. (a) Let p be prime. Suppose a and b are integers such t
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Description: please do 8 7. (a) Let p be prime. Suppose a and b are integers such that ab = 0(mod p). Show that either a = 0 or b = 0 (mod p).(b) Show that if a, 6, n are integers with nlab and gcd(a, n) = 1, thenn|b.8. Let p 2 3 be prime. Show that the only solu

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 13E

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