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Benelux
2009 Benelux
2
2
Part of
2009 Benelux
Problems
(1)
Generalization of ISL 2008 problem
Source: Benelux 2009
1/29/2011
Let
n
n
n
be a positive integer and let
k
k
k
be an odd positive integer. Moreover, let
a
,
b
a,b
a
,
b
and
c
c
c
be integers (not necessarily positive) satisfying the equations
a
n
+
k
b
=
b
n
+
k
c
=
c
n
+
k
a
a^n+kb=b^n+kc=c^n+ka
a
n
+
kb
=
b
n
+
k
c
=
c
n
+
ka
Prove that
a
=
b
=
c
a=b=c
a
=
b
=
c
.
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