n=8k+2
n=14l+8
n=21m+15
n+6=8k+2+6=8k+8=8s
n+6=14l+8+6=14l+14=14p
n+6=21m+15+6=21m+21=21q
n+6 =cmmmc (8,14,21)*r
8=2³
14=2*7
21=3*7
cmmmc (8,14,21)=(2³)*3*7=8*21=168
n+6=168r
n=168r-6
30|168r-6
30=2*3*5
3|168r-6 ∀r∈N*, pt ca 3|168 si 3|6
2|168r-6 ∀r∈N* pt ca 2|168 si 2|6
ramane deci ca 5|168r-6
⇒U (168r-6) ∈{0, 5}
⇒U (168r)∈{6; 1}
cum U (8 x)∈{ 8,4,2,6,0}⇒U(168r)={6; 1}∩{ 8,4,2,6,0}={6}
r minim=2, pt ca 8*2=16
numarul minim de forma 168r-6 care se va imparti la 30 este
168*2-6=330, cerinta
Obs urmatorul numar a fi fost 168*7-6=1170
