Question Number 70022 by naka3546 last updated on 30/Sep/19
$${Find}\:\:\:{all}\:\:{pairs}\:\:{of}\:\:\:\left({p},\:{q}\right)\:\:{integer}\left({s}\right)\:\:{such}\:\:{that} \\ $$$${p}^{\mathrm{3}} \:−\:{q}^{\mathrm{5}} \:\:=\:\:\left({p}\:+\:{q}\right)^{\mathrm{2}} \\ $$
Commented by MJS last updated on 30/Sep/19
$${p}=\mathrm{0}\:{q}=\mathrm{0} \\ $$$${p}=\mathrm{0}\:{q}=−\mathrm{1} \\ $$$${p}=\mathrm{1}\:{q}=\mathrm{0} \\ $$$${p}=\mathrm{7}\:{q}=\mathrm{3} \\ $$$$\mathrm{no}\:\mathrm{other}\:\mathrm{solution}\:\mathrm{for}\:−\mathrm{100}\leqslant{p},\:{q}\leqslant\mathrm{100} \\ $$