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Lusophon Mathematical Olympiad
2022 Lusophon Mathematical Olympiad
4
4
Part of
2022 Lusophon Mathematical Olympiad
Problems
(1)
Long Diophantine Equation
Source: Lusophon Mathematical Olympiad 2022 Problem 4
11/3/2022
How many integer solutions exist that satisfy this equation?
x
+
4
y
−
343
x
−
686
y
+
4
x
y
+
2022
=
0
x+4y-343\sqrt{x}-686\sqrt{y}+4\sqrt{xy}+2022=0
x
+
4
y
−
343
x
−
686
y
+
4
x
y
+
2022
=
0
.
number theory
Diophantine equation