Explicație pas cu pas:
x=(4n²+5)/(2n+1)
x€Z => (4n²+5)/(2n+1)€Z<=>
2n+1|4n²+5
2n+1|2n+1=> 2n+1|4n²+2n
Le scadem:
2n+1|4n²+2n-4n²-5 => 2n+1|2n-5
2n+1|2n-5
2n+1|2n+1
Le scadem:
2n+1|2n+1-2n+5 => 2n+1|6 => 2n+1€D6 In Z => 2n+1€{-6,-3,-2,-1,1,2,3,6} =>
2n€{-7,-4,-3,-2,0,1,2,4} =>
n€{-7/2,-2,-3/2,-1,0,1/2,1,2}
n€Z =>n€{-2,-1,0,1,2}
S={-2,-1,0,1} (pentru 2 nu merge) deci avem 4 elemente
