Question

VA ROG SA EXPLICATI CUM ATI FACUT !
1. Aflati toate numerele naturale de trei cifre care impartite la 11 dau restul 3 si impartite la 10 dau restul 2.
2. Aflati numerele naturale mai mici decat 3500 , care impartite la 10 , 17 si 19 dau acelasi rest.

Answer 1

x:11=c rest 3⇒   x=11c+3   ⇒  x+8=11c+3+8   ⇒  x+8=11c+11
x:10=c rest2   ⇒ x=10x+2   ⇒  c+8=10c+2+8    ⇒ x+8=10x+ 10

x+8∈M[11,10]
[11,10]=11·10=110
M[110]={0,110,220,330,440,550,660,770,880,990....
x+8=110⇒x=110-8=102
102:11=9 rest 3
102:10=10 rest 2
x+8=220⇒ x=220-8
x=212
212:11=19 rest 3
212:10=21 rest 3
...........
x+8=990⇒x=990-8
x=982
982:11=89 rest3
982:10=98 rest2
nr,sunt:102, 212,324,432,542,652,762,872,982