Question

Care numar impartit pe rand la 36,48,120 fiecare data da restul 3 ? Repede!!

Answer 1

Fie x = nr căutat

x:36=c1 rest 3
x:48=c2 rest 3
x:120=c3 rest 3
x=?
D=C•Î+R

x=36c1+3 => x-3=36c1 => (x-3) divizibil cu 36
x=48c2+3 => x-3=48c2 => (x-3) divizibil cu 48
x=120c3+3 => x-3=120c3 => (x-3) divizibil cu 120
=> x=c.m.m.m.c. al nr. 36;48;120

36=2²•3²
48=2⁴•3
120=2³•3•5
—————–
[36;48;120]=2⁴•3²•5=720

x-3=720 <=> x=723