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Austrian-Polish
1999 Austrian-Polish Competition
7
x^{x+y} =y^{y-x} diophantine
x^{x+y} =y^{y-x} diophantine
Source: Austrian - Polish 1999 APMC
May 4, 2020
diophantine
Diophantine equation
number theory
Problem Statement
Find all pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of positive integers such that
x
x
+
y
=
y
y
ā
x
x^{x+y} =y^{y-x}
x
x
+
y
=
y
y
ā
x
.
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