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Korea Junior Mathematics Olympiad
2022 Korea Junior Math Olympiad
8
Rational Number Theory
Rational Number Theory
Source: KJMO 2022 P8
October 29, 2022
number theory
rational number
Diophantine equation
Pythagorean Triple
Discriminant
Problem Statement
Find all pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
of rational numbers such that
x
y
2
=
x
2
+
2
x
ā
3
xy^2=x^2+2x-3
x
y
2
=
x
2
+
2
x
ā
3
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