Solution Found!
For the statement, determine whether the
Chapter 4, Problem 30E(choose chapter or problem)
For each statement in 19–31, determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterexample if it is false.
For all integers \(a\) and \(n\), if \(\text { a } \mid n^{2}\) and \(\mathrm{a} \leq \mathrm{n}\) then \(\mathrm{a} \mid \mathrm{n}\).
Questions & Answers
QUESTION:
For each statement in 19–31, determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterexample if it is false.
For all integers \(a\) and \(n\), if \(\text { a } \mid n^{2}\) and \(\mathrm{a} \leq \mathrm{n}\) then \(\mathrm{a} \mid \mathrm{n}\).
ANSWER:Step 1 of 2
In the questions where the statement needed to be proved that they are true or not, take any example and prove the following condition is true or not.
The objective is to determine whether the following statement is true or false:.
The statement is “For all integers a and n, if \(\left. a \right|{n^2}\) and \(a \le n$ then $\left. a \right|n\).”