If ne Z, then n² + 3n+ 4 is even.
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
How can we use cases to prove that these questions are even?

Transcribed Image Text:**Mathematics Exploration: Parity of Integers**
**Proposition**
If two integers have opposite parity, then their sum is odd.
---
**Additional Problems**
1. **Problem 1**
If \( n \in \mathbb{Z} \), then \( n^2 + 3n + 4 \) is even.
*(Use cases.)*
2. **Problem 2**
If two integers have opposite parity, then their product is even.
*(Use cases, and the phrase "without loss of generality.")*
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