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* Take as given that any integer n can be written in one of the forms: n = 3k or n = 3k + 1 or n = 3k +2 for some integer k (i.e. when dividing n by k the remainder is either 0, or 1, or 2). Show that if n and m are integers and neither is a multiple of 3, then nm also isn't a multiple of 3. (Hint: you will need to consider a small number of cases in your proof)

* Take as given that any integer n can be written in one of the forms: n = 3k or n = 3k + 1 or n = 3k +2 for some integer k (i.e. when dividing n by k the remainder is either 0, or 1, or 2). Show that if n and m are integers and neither is a multiple of 3, then nm also isn't a multiple of 3. (Hint: you will need to consider a small number of cases in your proof)

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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3.* Take as given that any integer n can be written in one of the forms: n = 3k or n = 3k + 1 or n = 3k + 2 for some integer k (i.e. when dividing n by k the remainder is either 0, or 1, or 2). Show that if n and m are integers and neither is a multiple of 3, then nm also isn't a multiple of 3. (Hint: you will need to consider a small number of cases in your proof)
Transcribed Image Text:3.* Take as given that any integer n can be written in one of the forms: n = 3k or n = 3k + 1 or n = 3k + 2 for some integer k (i.e. when dividing n by k the remainder is either 0, or 1, or 2). Show that if n and m are integers and neither is a multiple of 3, then nm also isn't a multiple of 3. (Hint: you will need to consider a small number of cases in your proof)
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