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21. For each divisor k > 1 of n, let U₁ (n) = {x € U(n): x mod k = 1}. For example U3 (21) = {1, 4, 10, 13, 16, 19}. List the element of U,(21) and show that U₂ (21) is a subgroup of U(21).

21. For each divisor k > 1 of n, let U₁ (n) = {x € U(n): x mod k = 1}. For example U3 (21) = {1, 4, 10, 13, 16, 19}. List the element of U,(21) and show that U₂ (21) is a subgroup of U(21).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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21. For each divisor k > 1 of n, let U₁ (n) = {x € U(n): x mod k = 1}. For example U3 (21) = {1, 4, 10, 13, 16, 19}. List the element of U₂ (21) and show that U₂ (21) is a subgroup of U(21). (Hint: build the Cayley table of U,(21) )
Transcribed Image Text:21. For each divisor k > 1 of n, let U₁ (n) = {x € U(n): x mod k = 1}. For example U3 (21) = {1, 4, 10, 13, 16, 19}. List the element of U₂ (21) and show that U₂ (21) is a subgroup of U(21). (Hint: build the Cayley table of U,(21) )
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