Question

Va rog frumos sa ma ajutati!!

Answer 1

$\frac{n+5}{n+1}$∈N deci n+1 I n+5 dar n+1 I n+1 deci 
n+1 I 4 adica n+1∈D₄(divizorii naturali ai lui 4)
D₄={1,2,4}
1.n+1=1⇒n=0
2.n+1=2⇒n=1
3.n+1=4⇒n=3
deci n={0;1;3}

Answer 2

(n+5):(n+1)=1 rest 4
n+5=1*(n+1)+4
$\frac{n+5}{n+1}=1+\frac{4}{n+1}\\O\ solutie\ este\ 1$
n+1∈D4
D4∈{1;2;4}
n+1=1⇒n=0
n+1=2⇒n=1
n+1=4⇒n=3
n∈{0;1;3}