[tex]Pentru~ca~\frac{27}{2x+1} \in N~trebuie~ca~27~sa~fie~divizibil~cu~(2x+1).~Adica~(2x+1)~sa~apartina~multimii~divizorilor~naturali~ai~lui~27.\\\\ D_{27}=\{1,~3,~9,~27\}\\\\ Cazul~I:~2x+1=1~|-1 \Rightarrow 2x=0~|:2\Rightarrow x=0\\\\ Cazul~II:~2x+1=3~|-1 \Rightarrow 2x=2~|:2\Rightarrow x=1\\\\ Cazul~III:~2x+1=9~|-1 \Rightarrow 2x=8~|:2\Rightarrow x=4\\\\ Cazul~IV:~2x+1=27~|-1 \Rightarrow 2x=26~|:2\Rightarrow x=13\\\\ \Rightarrow x \in \{0,~1,~4,~13\}\\\\ x \in N \\\\ \Rightarrow E=\{0,~1,~4,~13\}[/tex]
