Question Number 63636 by naka3546 last updated on 06/Jul/19
$${Find}\:\:{all}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y},\:{a},\:{b}\right)\:\:{for}\:\:{these}\:\:{equations}\:: \\ $$$$\:\:\:\:\:\:\:\:{x}\:+\:{y}^{\mathrm{2}} \:\:=\:\:{p}^{{a}} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} \:+\:{y}\:\:=\:\:{p}^{{b}} \\ $$$${which}\:\:\:{x},\:{y},\:{a},\:{b}\:\:{are}\:\:{integers}\:\:{and}\:\:{p}\:\:{prime}\:\:{number}\:. \\ $$