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2023 German National Olympiad
4
Cyclic system of two equations in three variables
Cyclic system of two equations in three variables
Source: Germany 2023, Problem 4
June 16, 2023
algebra
system of equations
algebra proposed
cyclic system
Problem Statement
Determine all triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
of real numbers with
a
+
4
b
=
b
+
4
c
=
c
+
4
a
.
a+\frac{4}{b}=b+\frac{4}{c}=c+\frac{4}{a}.
a
+
b
4
=
b
+
c
4
=
c
+
a
4
.
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