Question

Determinati cel mai mic numar natural care impartit pe rand cu 24,48,40 da de fiecare data restul 17 si caturi nenule.

Answer 1

x:24=c rest 17    ⇒x=24c+17     ⇒   x-17=24c+17-17     ⇒x-17=24c
x:48=c rest 17    ⇒x=48c+17     ⇒   x-17=48c+17-17     ⇒x-17=48c
x:40=c rest 17    ⇒x=40c+17     ⇒   x-17=40c+17-17     ⇒x-17=40c

x-17∈M[24,48,40]
24=2³·3
48=2⁴·3
40=2³·5
[24,48,40]=2⁴·3·5=240
M[240]={240, 480, 720......}
x-17=240
x=240+17
x=257
257:24=10 rest 17
257:48=5 rest 17
257:40=6 rest 17
cel mai mic nr.care indeplineste conditia este nr.257