Find-all-solutions-of-x-y-a-b-for-these-equations-x-y-2-p-a-x-2-y-p-b-which-x-y-a-b-are-integers-and-p-prime-number-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 63636 by naka3546 last updated on 06/Jul/19

Find all solutions of (x, y, a, b) for these equations : x + y^2 = p^a x^2 + y = p^b which x, y, a, b are integers and p prime number .

$${Find}\:\:{all}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y},\:{a},\:{b}\right)\:\:{for}\:\:{these}\:\:{equations}\:: \\ $$$$\:\:\:\:\:\:\:\:{x}\:+\:{y}^{\mathrm{2}} \:\:=\:\:{p}^{{a}} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} \:+\:{y}\:\:=\:\:{p}^{{b}} \\ $$$${which}\:\:\:{x},\:{y},\:{a},\:{b}\:\:{are}\:\:{integers}\:\:{and}\:\:{p}\:\:{prime}\:\:{number}\:. \\ $$

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Find-all-solutions-of-x-y-a-b-for-these-equations-x-y-2-p-a-x-2-y-p-b-which-x-y-a-b-are-integers-and-p-prime-number-

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