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Description: 4.7 using k and j if necessary. In complete sentences please. 4.6. Let a E Z. Prove that if 3 2a, then 3a.4.7. Let n E Z. Prove that 3 (2n2 + 1) if and only if 3 n.4.8. Let x € Z. Prove that if 2| (x² – 5), then 4| (x² – 5).

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4.6. Let a e Z. Prove that if 3|2a, then 3|a. 4.7. Let n E Z. Prove that 3 (2n² + 1) if and only if 3 ł n. 4.8. Let x E Z. Prove that if 2| (x – 5), then 4| (x² - 5).

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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Concept explainers

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Question

4.7 using k and j if necessary. In complete sentences please.

4.6. Let a E Z. Prove that if 3 2a, then 3a.
4.7. Let n E Z. Prove that 3 (2n2 + 1) if and only if 3 n.
4.8. Let x € Z. Prove that if 2| (x² – 5), then 4| (x² – 5).

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