Question

Determinati nemerele naturale cuprinse intre 200 si 600 care, impartite la 8, 12 si 15, dau resturile 6, 10, 13​

Answer 1

Răspuns:

Explicație pas cu pas:

n = 8C1 + 6

n = 12C2 + 10

n = 15C3 + 13

n + 2 = 8C1 + 6 + 2 = 8C1 + 8 = 8(C1 + 1)

n + 2 = 12C2 + 10 + 2 = 12C2 + 12 = 12(C2 + 1)

n + 2 = 15C3 + 13 + 2 = 15C3 + 15 = 15(C3 + 1)

8 = 2^3

12 = 2^2*3

15 = 3*5

cmmmc (8, 12, 15) = 2^3*3*5 = 8*3*5 = 120

n + 2 = 240; 360; 480

n = 238; 358; 478