Question

Determinați n ∈ N pentru care (2n + 1)│(6n + 24).

Answer 1

(2n+1) | (6n + 24)

(2n+1) | 3( 2n+1) => (2n+1) | (6n + 3)

Din (2n+1) | (6n + 24) si (2n+1) | (6n + 3) => (2n+1)|(6n+24) - (6n+3) =>(2n+1) | 21

D21 = { 1, 3, 7, 21 }

Caz 1 : 2n+1 = 1 => 2n = 0 => n= 0

Caz 2: 2n+1 = 3 => 2n = 2 => n = 1

Caz 3: 2n+1 = 7 => 2n = 6 => n = 3

Caz 4: 2n+1= 21 => 2n = 20 => n=10

n={0, 1, 3, 10}