[tex]\dfrac{a}{7}=\dfrac{2}{2b+1}\\
a\cdot (2b+1)=14\\
\text{De aici se deduc mai multe cazuri :}\\
\left \{ {{a=1} \atop {2b+1=14}} \right. \Leftrightarrow \left \{ {{a=1} \atop {b=\frac{13}{2}}\notin \mathbb{N}(\text{nu convine})} \right. \\
\\
\left \{ {{a=2} \atop {2b+1=7}} \right. \Leftrightarrow \left \{ {{a=2} \atop {b=3}} \right. \\
\\
\left \{ {{a=7} \atop {2b+1=2}} \right. \Leftrightarrow \left \{ {{a=7} \atop {b=\frac{1}{2}\notin \mathbb{N}(\text{nu convine})}} \right. \\
[/tex]
[tex] \left \{ {{a=14} \atop {2b+1=1}} \right.\\
\text{Nici aceasta nu convine,deoarece a trebuie sa fie o cifra.}\\
\text{Singura solutie este:}\\
S:\overline{ab}=23 [/tex]
