Question

Aflati numerele de trei cifre impartite pe rand la 24 , 36 , 48 dau de fiecare data restul 17 .

Answer 1

x;24=c rest 17   ⇒x=24c+17⇒x-17=24c+17-17⇒x-17=24c
x:36=c rest 17   ⇒x=36c+17⇒x-17=36c+17-17⇒x-17=36c
x:48=c rest 17   ⇒x=48c+17⇒x-17=48c+17-17⇒x-17=48c

⇒x-17∈M[24,36,48}
24=2³·3
36=2²·3²
48=2⁴·3
[24,36,48]=2⁴·3²=144
M[144]={144, 288, .....}
x-17=144
x=144+17
x=161
161:24=6 rest 17
161:36=4 rest17
161:48=3 rest 17