4. (i) Show that 2 is a primitive root mod 11² = 121. Hint: Use the criterion given by Lemma 6.4 and a calculator. Conclude that 2 is a primitive root mod 11e for any e. (ii) How many elements of order 5 are there in the group U1331? Note that 1331 = 11³. (iii) Find all elements of order 5 in U1331.
4. (i) Show that 2 is a primitive root mod 11² = 121. Hint: Use the criterion given by Lemma 6.4 and a calculator. Conclude that 2 is a primitive root mod 11e for any e. (ii) How many elements of order 5 are there in the group U1331? Note that 1331 = 11³. (iii) Find all elements of order 5 in U1331.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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[Number Theory] How do you solve question 4? The second picture is for definitions. Thank you!
Additional information:
- We say that a group G is abelian if its elements commute, that is, gh = hg for all g, h in G
- Un is an abelian group under multiplication mod (n)
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