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A symmetric pair of functions?
A symmetric pair of functions?
Source: Brazil EGMO TST 2023 #2
November 10, 2022
algebra
Problem Statement
Determine all the integers solutions
(
x
,
y
)
(x,y)
(
x
,
y
)
of the following equation
x
2
−
4
2
x
−
1
+
y
2
−
4
2
y
−
1
=
x
+
y
\frac{x^2-4}{2x-1}+\frac{y^2-4}{2y-1}=x+y
2
x
−
1
x
2
−
4
+
2
y
−
1
y
2
−
4
=
x
+
y
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