Question

Answer 1

9:

\(n^2+n-17⋮n+5\)

=>\(n^2+5n-4n-20+3⋮n+5\)

=>\(n+5\inƯ\left(3\right)\)

=>\(n+5\in\left\{1;-1;3;-3\right\}\)

=>\(n\in\left\{-4;-6;-2;-8\right\}\)

mà n là số tự nhiên

nên \(n\in\varnothing\)

8:

\(2n^2+n-6⋮2n+1\)

=>\(2n+1\inƯ\left(-6\right)\)

=>\(2n+1\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

mà n nguyên

nên \(2n+1\in\left\{1;-1;3;-3\right\}\)

=>\(2n\in\left\{0;-2;2;-4\right\}\)

=>\(n\in\left\{0;-1;1;-2\right\}\)

7:

\(\overline{ab}+\overline{ba}=10a+b+10b=a=11a+11b=11\left(a+b\right)⋮11\)

3:

\(A=16^5+2^{15}\)

\(=2^{20}+2^{15}\)

\(=2^{15}\left(2^5+1\right)=2^{15}\cdot33⋮33\)