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Long Diophantine Equation

Source: Lusophon Mathematical Olympiad 2022 Problem 4

November 3, 2022
number theoryDiophantine equation

Problem Statement

How many integer solutions exist that satisfy this equation?
x+4y−343x−686y+4xy+2022=0x+4y-343\sqrt{x}-686\sqrt{y}+4\sqrt{xy}+2022=0.
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