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42. (a) Let a, b, c e Z with (a, b) = (a, c) = 1. Prove that (a, bc) = 1. %3D 22 Chapter 1 Divisibility and Factorization (b) Let a, b1, b2, ... , b, eZ with (a, b¡) = (a, b2) = ..: = (a, b,) = 1. %3D Prove that

42. (a) Let a, b, c e Z with (a, b) = (a, c) = 1. Prove that (a, bc) = 1. %3D 22 Chapter 1 Divisibility and Factorization (b) Let a, b1, b2, ... , b, eZ with (a, b¡) = (a, b2) = ..: = (a, b,) = 1. %3D Prove that

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 12EQ
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Find out how to Prove both cases below. 42 a) & 42 b)

 

p.s.~I was a bit stuck on how to start it.

42. (a) Let a, b, ce Z with (a, b) = (a, c) = 1. Prove that (a, bc) = 1. 22 Chapter 1 Divisibility and Factorization (b) Let a, b1, b2, ... , b, eZ with (a, b1) = (a, b2) Prove that (а, b») 3D 1. (a, b,b2 · · · b„) = 1
Transcribed Image Text:42. (a) Let a, b, ce Z with (a, b) = (a, c) = 1. Prove that (a, bc) = 1. 22 Chapter 1 Divisibility and Factorization (b) Let a, b1, b2, ... , b, eZ with (a, b1) = (a, b2) Prove that (а, b») 3D 1. (a, b,b2 · · · b„) = 1
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