Question

Sa se determine valorile naturale ale lui n  pentru care: a) 3n+9/2n+1 apartine lui N

Answer 1

(3n+9)/(2n+1) ∈N
n∈N                          =>

=>(2n+1)|(3n+9)        <=> (2n+1)|2(3n+9)
    (2n+1)|(2n+1)                (2n+1)|3(2n+1)      <=>

<=> (2n+1)|(6n+18)
        (2n+1)|(6n+3)          <=> (2n+1)| 6n+18-6n-3  <=> (2n+1)|15  =>

=>(2n+1)={1,3,5,15}

1) 2n+1= 1 <=> 2n=0  =>n=0

2) 2n+1=3  <=> 2n=2  =>n=1

3) 2n+1=5  <=> 2n=4  =>n=2

4) 2n+1=15 <=> 2n=14 =>n=7

n={0,1,2,7}