Question

Determinati x ∈ N astfel incat urmatoarele numere sa fie naturale :
1. 5 supra x
2. 9 supra x-1
3. 10 supra x+1
4. 13 supra x-7
5. 6 supra x(x-1)

Answer 1

1. 5 e nr prim, deci se divide numai prin el si prin 1
Adica
    5/x=1  => x=5 ∈N  
si  5/x=5  => x=1 ∈N            x={1,5}

2. 9/(x-1). Divizorii lui 9 sunt D9={1,3,9}
x-1=1 => x=2 ∈N
x-1=3 => x=4 ∈N
x-1=9 => x=10∈N    Deci x={2,4,10}

3. 10/(x+1). D10={1,2,5,10}
x+1=1 => x=0 ∈N
x+1=2 => x=1 ∈N
x+1=5 => x=4 ∈N
x+1=10 => x=9∈N    x={0,1,4,9}

4. 13/(x-7) D13={1,13}
x-7=1 => x=8∈N
x-7=13 => x=20∈N   x={8,20}

5. 6/x(x-1)  D6={1,2,3,6}
x(x-1)=1 => x nu are solutii naturale
x(x-1)=2 =>  x=2∈N
x(x-1)=3 =>  x nu are solutii naturale
x(x-1)=6 =>  x=3 ∈N       x={2,3}