Question

Determinati cel mai mic numar natural diferit de 0 care impartit la 12,28 si,respectiv,36 da de fiecare data restul 7.

Answer 1

x:12=c rest 7   ⇒x=12c+7             ⇒x-7=12c+7-7    ⇒x-7=12c
x:28=c rest 7   ⇒x=28c+7             ⇒x-7=28c+7-7    ⇒x-7=28c
x:36=c rest 7   ⇒x=36c+7             ⇒x-7=36c+7-7⇒    x-7=36c

x-7=M[12,28,36]
12=2²·3
28=2²·7
36=2²·3²
{12,28,36]=2²·3²·7=252
M[252]={252, 504......}
x-7=252
x=252+7
x=259 este cel mai mic nr
259:12=21 rest 7
259:28=9 rest 7
259:36=7 rest 7