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Question Number 159249 by henderson last updated on 14/Nov/21

$$\mathbf{hi}!$$$$\mathbf{solve}\mathbf{in}\mathbf{IN}\times \mathbf{IN}\mathbf{this}\mathbf{one}:(\mathit{x}+1)(\mathit{y}+2)=2\mathit{x}\mathit{y}.$$$$\mathbf{thanks}.$$

Answered by FongXD last updated on 14/Nov/21

$$\iff 2\mathrm{x}+2+(\mathrm{x}+1)\mathrm{y}=2\mathrm{xy}$$$$\Rightarrow \mathrm{y}=\frac{2\mathrm{x}+2}{\mathrm{x}-1}=2+\frac{4}{\mathrm{x}-1}\in \mathbb{N}$$$$\Rightarrow \{\begin{array}{l}\mathrm{x}-1=1\\ \mathrm{x}-1=2\\ \mathrm{x}-1=4\end{array}$$$$\bullet \mathrm{x}=2,\mathrm{y}=6$$$$\bullet \mathrm{x}=3,\mathrm{y}=4$$$$\bullet \mathrm{x}=5,\mathrm{y}=3$$

Commented by Rasheed.Sindhi last updated on 15/Nov/21

$$\cap \mathrm{i}\subset \in !$$

Commented by henderson last updated on 15/Nov/21

$$\mathbf{thanks},\mathbf{Sir}\mathbf{FongXD}!$$

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