Question

Aflati cel mai mic numar care impartit pe rand la 5, 17 si 19, da de fiecare data restul 4.

Answer 1

x - 4 = [5, 17, 19] ⇒ x = 5·17·19 + 4

Answer 2

x:5=c1 rest 4
x=5*c1+4
x-4=5*c1
x-4=M5
x:17=c2 rest 4
x=17*c2+4
x-4=17*c2
x-4=M17
x:19=c3 rest 4
x=19*c3+4
x-4=19*c3
x-4=M19
Deci:
x-4=M5∩M17∩M19
x-4=M(5,17,19)
x-4=cmmmc(5,17,19)
Descompunem numerele 5,17,19 in factori primi
5/5
1/
5=1*5
17/17
1/
17=1*17
19/19
1/
19=1*19
Se iau toti factorii primi la puterile cele mai mari.
cmmmc(5,17,19)=5*17*19=1615
x-4=1615
x=1615+4
x=1619