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Show that Zn is cyclic for any integer n> 1 by identifying a number a such that (a) = Zn. For n > 2, show that Zn has at least 2 generators by finding a number bn such that (bn) = Zn.

Show that Zn is cyclic for any integer n> 1 by identifying a number a such that (a) = Zn. For n > 2, show that Zn has at least 2 generators by finding a number bn such that (bn) = Zn.

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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Please do part A and B and please show step by step and explain

**Exercise 15.5.10.** (a) Show that \( \mathbb{Z}_n \) is cyclic for any integer \( n > 1 \) by identifying a number \( a \) such that \( \langle a \rangle = \mathbb{Z}_n \). (b) For \( n > 2 \), show that \( \mathbb{Z}_n \) has at least 2 generators by finding a number \( b_n \) such that \( \langle b_n \rangle = \mathbb{Z}_n \).
Transcribed Image Text:**Exercise 15.5.10.** (a) Show that \( \mathbb{Z}_n \) is cyclic for any integer \( n > 1 \) by identifying a number \( a \) such that \( \langle a \rangle = \mathbb{Z}_n \). (b) For \( n > 2 \), show that \( \mathbb{Z}_n \) has at least 2 generators by finding a number \( b_n \) such that \( \langle b_n \rangle = \mathbb{Z}_n \).
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