Răspuns :
(4n+8-8)/(n+2)∈N
(4n+8)/(n+2)-8/(n+2)∈N
4-8/(n+2)∈N
8/(n+2)∈{0;1;2;3;4}
8/(n+2)=0,n∉N
8/(n+2)=1...n+2=8...n=6
8/(n+2)=2...n+2=4...n=2
8/(n+2)=3....3n+6=8...n∉N
8/(n+2)=4....4n+8=8....n=0
n∈{0;2;6}
Altfel
n+2∈D8N={1;2;4;8}
n∈{-1;0;2;6}∩N={0;2;6}care verifica fiecare (verificare directa)
(4n+8)/(n+2)-8/(n+2)∈N
4-8/(n+2)∈N
8/(n+2)∈{0;1;2;3;4}
8/(n+2)=0,n∉N
8/(n+2)=1...n+2=8...n=6
8/(n+2)=2...n+2=4...n=2
8/(n+2)=3....3n+6=8...n∉N
8/(n+2)=4....4n+8=8....n=0
n∈{0;2;6}
Altfel
n+2∈D8N={1;2;4;8}
n∈{-1;0;2;6}∩N={0;2;6}care verifica fiecare (verificare directa)