Answered: 1. Let a and b be integers. Prove that…

1. Let a and b be integers. Prove that GCD(a,b) divides GCD(a+b, a−b). Give an example when GCD(a,b) not equals to GCD(a+b, a−b).

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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Question

1. Let a and b be integers. Prove that GCD(a,b) divides GCD(a+b, a−b). Give an example when GCD(a,b) not equals to GCD(a+b, a−b).
2. Let n be an integer. Prove that GCD(n²−n+1, n+1) equals 1 or 3. Show by examples that both values are possible.

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