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(a) For all integers n and m, if n +3m is even, then n²+3n+3nm +9m +1 is odd.

(a) For all integers n and m, if n +3m is even, then n²+3n+3nm +9m +1 is odd.

Advanced Engineering Mathematics
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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prove or disprove that this statement is even(ignore that it says odd, it's a typo).

**Problem Statement:** (a) For all integers \( n \) and \( m \), if \( n + 3m \) is even, then \( n^2 + 3n + 3nm + 9m + 1 \) is odd. --- **Explanation:** This problem involves properties of even and odd numbers in algebraic expressions. Specifically, it asserts that under the condition where the sum \( n + 3m \) is even, the expression \( n^2 + 3n + 3nm + 9m + 1 \) will be odd. Understanding this requires knowledge of how integer addition and multiplication impact even and odd outcomes.
Transcribed Image Text:**Problem Statement:** (a) For all integers \( n \) and \( m \), if \( n + 3m \) is even, then \( n^2 + 3n + 3nm + 9m + 1 \) is odd. --- **Explanation:** This problem involves properties of even and odd numbers in algebraic expressions. Specifically, it asserts that under the condition where the sum \( n + 3m \) is even, the expression \( n^2 + 3n + 3nm + 9m + 1 \) will be odd. Understanding this requires knowledge of how integer addition and multiplication impact even and odd outcomes.
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