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2022 Kosovo National Mathematical Olympiad
1
a+bc=b+ca=c+ab
a+bc=b+ca=c+ab
Source: Kosovo Mathematical Olympiad 2022, Grade 12, Problem 1
March 6, 2022
algebra
Problem Statement
Find all real numbers
a
,
b
a,b
a
,
b
and
c
c
c
such that
a
+
b
c
=
b
+
c
a
=
c
+
a
b
a+bc=b+ca=c+ab
a
+
b
c
=
b
+
c
a
=
c
+
ab
.
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