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Israel National Olympiad
2023 Israel National Olympiad
P4
P4
Part of
2023 Israel National Olympiad
Problems
(1)
System of equations with a parameter
Source: 2023 Israel National Olympiad P4
12/16/2022
For each positive integer
n
n
n
, find all triples
a
,
b
,
c
a,b,c
a
,
b
,
c
of real numbers for which
{
a
=
b
n
+
c
n
b
=
c
n
+
a
n
c
=
a
n
+
b
n
\begin{cases}a=b^n+c^n\\ b=c^n+a^n\\ c=a^n+b^n\end{cases}
⎩
⎨
⎧
a
=
b
n
+
c
n
b
=
c
n
+
a
n
c
=
a
n
+
b
n
algebra
system of equations
parameterization