1. (20 pts) Given n is a positive integer, prove that n is odd if and only if n² + 3 is even. You must use definitions of even (and odd, if needed). Do not use "even plus even is even" or similar rules of thumb.
1. (20 pts) Given n is a positive integer, prove that n is odd if and only if n² + 3 is even. You must use definitions of even (and odd, if needed). Do not use "even plus even is even" or similar rules of thumb.
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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Transcribed Image Text:1. (20 pts) Given n is a positive integer, prove that n is odd if and only if n² + 3 is even.
You must use definitions of even (and odd, if needed). Do not use "even plus even is even" or
similar rules of thumb.
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