[tex]\it a,\ b,\ c\in\mathbb{N},\ \ c=prim\ \ \ \ \ (1)\\ \\ \dfrac{7,5}{a}=\dfrac{b}{c} \Rightarrow \underbrace{a\cdot b}_{\in\mathbb{N}}=7,5c\Rightarrow 7,5\cdot c\in\mathbb{N}\Rightarrow c = par\ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow c=2\\ \\ a\cdot b=7,5\cdot c\Rightarrow a\cdot b=7,5\cdot2\Rightarrow a\cdot b=15 =1\cdot15=3\cdot5=5\cdot3=15\cdot1\\ \\ (a,\ b)\in\{(1,\ \ 15);\ \ (3,\ \ 5);\ \ (5,\ \ 3);\ \ (15,\ \ 1) \}[/tex]
