Question Number 112528 by dw last updated on 08/Sep/20
$${If}\:\:\:\:\:\frac{{n}−\mathrm{7}}{{n}−\mathrm{17}}\:\:\:\:\:\:\:{and}\:\:\:\:\frac{{n}−\mathrm{14}}{{n}−\mathrm{24}}\:\:\:{are}\:{integers}\:{numbers} \\ $$$${n}=? \\ $$
Commented by Dwaipayan Shikari last updated on 08/Sep/20
$$\mathrm{1}+\frac{\mathrm{10}}{{n}−\mathrm{17}}\:\:\:\:\:\:\:{n}\left(\mathrm{7},\mathrm{12},\mathrm{18},\mathrm{22},\mathrm{27}\right) \\ $$$$\frac{{n}−\mathrm{10}}{{n}−\mathrm{24}}=\mathrm{1}+\frac{\mathrm{14}}{{n}−\mathrm{24}}\:\:\:\:{n}\left(\mathrm{10},\mathrm{31},\mathrm{38}\right) \\ $$
Commented by Rasheed.Sindhi last updated on 09/Sep/20
$${No}\:{value}\:{of}\:{n}\:{for}\:{which}\:\frac{{n}−\mathrm{7}}{{n}−\mathrm{17}} \\ $$$$\&\:\frac{{n}−\mathrm{14}}{{n}−\mathrm{24}}\:{are}\:{simultaneously} \\ $$$${integers}. \\ $$