[tex]a-1 = \dfrac{10}{b}+3\\ \\ \\
a \in \mathbb_N $ $ \Rightarrow a-1 \in \mathbb_N $ $ \Rightarrow \\ \\ \Rightarrow \dfrac{10}{b} +3 \in \mathbb_N $ $ \Rightarrow \\ \\ \Rightarrow b | 10 \Rightarrow b \in D_{10} \Rightarrow b \in \Big\{1,2,5,10\Big\}\Big|^{-1} \Rightarrow \\ \\\Rightarrow \dfrac{1}{b} \in \Big\{1,\dfrac{1}{2},\dfrac{1}{5},\dfrac{1}{10}\Big\} \Big|\cdot 10 \Rightarrow \\ \\ \Rightarrow \dfrac{10}{b} \in \Big\{10,5,2,1\Big\}\Big|+3 \Rightarrow \\ \\ \Rightarrow \dfrac{10}{b}+3 \in \Big\{13,8,5,4\Big\} \Rightarrow \\ \\ \Rightarrow a-1 \in \Big\{13,8,5,4\Big\} |+1 \Rightarrow \\ \\ \Rightarrow \boxed{a\in \Big\{14,9,6,5\Big\}} \\ ~~~~~\boxed{b \in \Big\{1,2,5,10\Big\}}\\ \\ \\ \Rightarrow (a,b) \in \Big\{(14,1);(9,2);(6,5);(5,10)\Big\} [/tex]
