State and prove Euclid's Lemma. 3. Suppose ajb2 and gcd(a; b) = 1. (3) (a) Apply Euclid's Lemma to get the conclusion a = 1. (5) (b) Show that 2jb2 (i.e. b2 is even) and gcd(2; b) = 1 (i.e. b is odd) is a contradiction. This proves that if b2 is even, then b is even, without using the contrapositive.

State and prove Euclid's Lemma. 3. Suppose ajb2 and gcd(a; b) = 1. (3) (a) Apply Euclid's Lemma to get the conclusion a = 1. (5) (b) Show that 2jb2 (i.e. b2 is even) and gcd(2; b) = 1 (i.e. b is odd) is a contradiction. This proves that if b2 is even, then b is even, without using the contrapositive.

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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