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Question Number 11214 by uni last updated on 17/Mar/17

Answered by FilupS last updated on 17/Mar/17

$$a+\frac{b}{a}=4\Rightarrow b=a(4-a)$$$$\because a\in \mathbb{Z}\mathrm{and}\mathrm{RHS}\in \mathbb{Z},\therefore b\in \mathbb{Z}$$$$$$$$\therefore a=\frac{b}{4-a}$$$$\because a\in \mathbb{Z},\frac{b}{4-a}\in \mathbb{Z},\therefore (4-a)\mathrm{is}\mathrm{a}\mathrm{factor}$$

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