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Question Number 161843 by Rasheed.Sindhi last updated on 23/Dec/21

$$\text{You can't use 'macro parameter character \#' in math mode}$$$$\mathrm{Solve}\mathrm{for}\mathbf{integer}\mathrm{numbers}:$$$$\frac{\mathrm{x}}{\mathrm{y}}+\frac{5}{\mathrm{x}}+\frac{\mathrm{y}-5}{5}=\frac{\mathrm{y}+\mathrm{x}}{\mathrm{y}+5}+\frac{5+\mathrm{y}}{5+\mathrm{x}}$$

Commented by malwan last updated on 23/Dec/21

$$x=0orx=5$$$$thenwehaveoneequation$$$$andonevariabley$$

Commented by Rasheed.Sindhi last updated on 23/Dec/21

$$x\ne 0because{it}^{\prime }sindenominator.$$$$\text{You can't use 'macro parameter character \#' in math mode}$$

Commented by mr W last updated on 23/Dec/21

$$x\ne 0,x\ne -5,y\ne 0,y\ne -5$$$$wecanseex,ycould\left(butnotmust\right)$$$$bemultiplesof5,thenwecanget$$$$follwingsolutions:$$$$(5,5)$$$$(5,10)$$$$(-10,5)$$$$but{it}^{\prime }snoteasytoprovethatother$$$$\left(notmultiplesof5\right)solutions{don}^{\prime }t$$$$exist.$$

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