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Let n be an integer 2 ≤ n ≤ 24 and let m be any integer such that n|m². For which values of n is the following true If n/m², then nlm. It works for n = 2 but it does not work for n = 4 since 4|6² but 4 does not divide 6. Complete the following table True/False N 2 True 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 False True Counter example 4 10² but 4/10 Based on your table results make a general conjecture when it is true that is: If n|m², then n|m. That is what condition on n makes it work.

Let n be an integer 2 ≤ n ≤ 24 and let m be any integer such that n|m². For which values of n is the following true If n/m², then nlm. It works for n = 2 but it does not work for n = 4 since 4|6² but 4 does not divide 6. Complete the following table True/False N 2 True 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 False True Counter example 4 10² but 4/10 Based on your table results make a general conjecture when it is true that is: If n|m², then n|m. That is what condition on n makes it work.

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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Don’t have to prove the true statements just show an example of it working...

 

 

Let \( n \) be an integer \( 2 \leq n \leq 24 \) and let \( m \) be any integer such that \( n|m^2 \). For which values of \( n \) is the following true: If \( n|m^2 \), then \( n|m \). It works for \( n = 2 \) but it does not work for \( n = 4 \) since \( 4|6^2 \) but 4 does not divide 6. Complete the following table: \[ \begin{array}{|c|c|c|} \hline N & \text{True/False} & \text{Counter example} \\ \hline 2 & \text{True} & \\ 3 & & \\ 4 & \text{False} & 4|10^2 \text{ but } 4 \nmid 10 \\ 5 & & \\ 6 & \text{True} & \\ 7 & & \\ 8 & & \\ 9 & & \\ 10 & & \\ 11 & & \\ 12 & & \\ 13 & & \\ 14 & & \\ 15 & & \\ 16 & & \\ 17 & & \\ 18 & & \\ 19 & & \\ 20 & & \\ 21 & & \\ 22 & & \\ 23 & & \\ 24 & & \\ \hline \end{array} \] Based on your table results make a general conjecture when it is true that is: If \( n|m^2 \), then \( n|m \). That is what condition on \( n \) makes it work.
Transcribed Image Text:Let \( n \) be an integer \( 2 \leq n \leq 24 \) and let \( m \) be any integer such that \( n|m^2 \). For which values of \( n \) is the following true: If \( n|m^2 \), then \( n|m \). It works for \( n = 2 \) but it does not work for \( n = 4 \) since \( 4|6^2 \) but 4 does not divide 6. Complete the following table: \[ \begin{array}{|c|c|c|} \hline N & \text{True/False} & \text{Counter example} \\ \hline 2 & \text{True} & \\ 3 & & \\ 4 & \text{False} & 4|10^2 \text{ but } 4 \nmid 10 \\ 5 & & \\ 6 & \text{True} & \\ 7 & & \\ 8 & & \\ 9 & & \\ 10 & & \\ 11 & & \\ 12 & & \\ 13 & & \\ 14 & & \\ 15 & & \\ 16 & & \\ 17 & & \\ 18 & & \\ 19 & & \\ 20 & & \\ 21 & & \\ 22 & & \\ 23 & & \\ 24 & & \\ \hline \end{array} \] Based on your table results make a general conjecture when it is true that is: If \( n|m^2 \), then \( n|m \). That is what condition on \( n \) makes it work.
Expert Solution
Step 1: Analysis and Introduction

Given statements:

Let n be an integer in the interval 2 less or equal than n less or equal than 24.

Let m be any integer such that n vertical line m squared.

If n vertical line m squared, then n vertical line m.

To find:

The statement is true or false and give an example on it.


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