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Lusophon Mathematical Olympiad
2022 Lusophon Mathematical Olympiad
1
1
Part of
2022 Lusophon Mathematical Olympiad
Problems
(1)
Cyclic system of equations with three variables
Source: Lusophon Mathematical Olympiad 2022 Problem 1
11/3/2022
How many triples
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
with
a
,
b
,
c
∈
R
a,b,c \in \mathbb{R}
a
,
b
,
c
∈
R
satisfy the following system?
{
a
4
−
b
4
=
c
b
4
−
c
4
=
a
c
4
−
a
4
=
b
\begin{cases} a^4-b^4=c \\ b^4-c^4=a \\ c^4-a^4=b \end{cases}
⎩
⎨
⎧
a
4
−
b
4
=
c
b
4
−
c
4
=
a
c
4
−
a
4
=
b
.
algebra
system of equations