[tex]\dfrac{2x+1}{13}\in \mathbb_{N} $ $\Rightarrow 2x+1 \in M_{13} \Rightarrow 2x+1\in \Big\{13,26,39,52,...\Big\} \Rightarrow \\ \\ \Rightarrow 2x+1 = 13\cdot n,\quad n\in \mathbb_{N}$*\\ \\ $ 2x+1 = 13\cdot n \Big|-1\Rightarrow 2x = 13\cdot n-1 \Rightarrow x = \dfrac{13\cdot n-1}{2} \\ \\ x\in \mathbb_{N}$ \Rightarrow 13\cdot n-1 $ par $ \Rightarrow 13\cdot n -1 $ par $ $ doar atunci cand \\$ 13\cdot n$ impar \Rightarrow 13\cdot n $ impar $ $ doar atunci cand n impar\\ \\[/tex]
[tex] $ \Rightarrow n \in \Big\{1,3,5,7,9,11,...\Big\}\\ \\ \Rightarrow \x = \dfrac{13\cdot n-1}{2},\quad n\in \Big\{1,3,5,7,9,11,...\Big\} \Rightarrow \\ \\ \Rightarrow x\in \Big\{\dfrac{13-1}{2},\dfrac{39-1}{2},\dfrac{65-1}{2},\dfrac{91-1}{2},\dfrac{117-1}{2},\dfrac{143-1}{2},...\Big\} \Rightarrow \\ \\ \Rightarrow \boxed{x\in \Big\{6,19,32,45,58,71...\Big\}} \Rightarrow \\ \\ \\ \Rightarrow \boxed{x= \dfrac{13\cdot n-1}{2}, \quad n \in \mathbb_{N}$ \backslash $ $2\mathbb_{N}}[/tex]
[tex] \Big(\mathbb_{N}$ \backslash $ $2\mathbb_{N}$ $ \text{este multimea numerelor naturale impare.}\Big)[/tex]
