Question Number 159249 by henderson last updated on 14/Nov/21
$$\boldsymbol{\mathrm{hi}}\:! \\ $$$$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{IN}}×\boldsymbol{\mathrm{IN}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{one}}\::\:\left(\boldsymbol{{x}}+\mathrm{1}\right)\left(\boldsymbol{{y}}+\mathrm{2}\right)=\mathrm{2}\boldsymbol{{xy}}. \\ $$$$\boldsymbol{\mathrm{thanks}}. \\ $$
Answered by FongXD last updated on 14/Nov/21
$$\Leftrightarrow\:\mathrm{2x}+\mathrm{2}+\left(\mathrm{x}+\mathrm{1}\right)\mathrm{y}=\mathrm{2xy} \\ $$$$\Rightarrow\:\mathrm{y}=\frac{\mathrm{2x}+\mathrm{2}}{\mathrm{x}−\mathrm{1}}=\mathrm{2}+\frac{\mathrm{4}}{\mathrm{x}−\mathrm{1}}\in\mathbb{N} \\ $$$$\Rightarrow\:\begin{cases}{\mathrm{x}−\mathrm{1}=\mathrm{1}}\\{\mathrm{x}−\mathrm{1}=\mathrm{2}}\\{\mathrm{x}−\mathrm{1}=\mathrm{4}}\end{cases} \\ $$$$\bullet\:\mathrm{x}=\mathrm{2},\:\mathrm{y}=\mathrm{6} \\ $$$$\bullet\:\mathrm{x}=\mathrm{3},\:\mathrm{y}=\mathrm{4} \\ $$$$\bullet\:\mathrm{x}=\mathrm{5},\:\mathrm{y}=\mathrm{3} \\ $$
Commented by Rasheed.Sindhi last updated on 15/Nov/21
$$\cap\mathrm{i}\subset\in! \\ $$
Commented by henderson last updated on 15/Nov/21
$$\boldsymbol{\mathrm{thanks}},\:\boldsymbol{\mathrm{Sir}}\:\boldsymbol{\mathrm{FongXD}}\:! \\ $$