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National and Regional Contests
Spain Contests
Spain Mathematical Olympiad
2013 Spain Mathematical Olympiad
2
2
Part of
2013 Spain Mathematical Olympiad
Problems
(1)
x^n+y^n+z^n is constant
Source: Spanish Mathematical Olympiad 2013. Problem 2
3/26/2015
Find all the possible values of a positive integer
n
n
n
for which the expression
S
n
=
x
n
+
y
n
+
z
n
S_n=x^n+y^n+z^n
S
n
=
x
n
+
y
n
+
z
n
is constant for all real
x
,
y
,
z
x,y,z
x
,
y
,
z
with
x
y
z
=
1
xyz=1
x
yz
=
1
and
x
+
y
+
z
=
0
x+y+z=0
x
+
y
+
z
=
0
.
algebra