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Make sure that all your answers are explained carefully. (a) Remember that the order k = ordma is the smallest positive integer for which ak 1 mod m. Determine the order of 11 modulo 21. (b) For each of the following positive integers, say whether it has a primitive root or not. Explain why. (i) a = 19, (ii) b = 250, (iii) d = 45.

Make sure that all your answers are explained carefully. (a) Remember that the order k = ordma is the smallest positive integer for which ak 1 mod m. Determine the order of 11 modulo 21. (b) For each of the following positive integers, say whether it has a primitive root or not. Explain why. (i) a = 19, (ii) b = 250, (iii) d = 45.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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Question 4 Make sure that all your answers are explained carefully. (a) Remember that the order k = ordma is the smallest positive integer for which a = 1 mod m. Determine the order of 11 modulo 21. (b) For each of the following positive integers, say whether it has a primitive root or not. Explain why. (i) a = 19, (ii) b = 250, (iii) d = 45. 1
Transcribed Image Text:Question 4 Make sure that all your answers are explained carefully. (a) Remember that the order k = ordma is the smallest positive integer for which a = 1 mod m. Determine the order of 11 modulo 21. (b) For each of the following positive integers, say whether it has a primitive root or not. Explain why. (i) a = 19, (ii) b = 250, (iii) d = 45. 1
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