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USAMO
1982
Problem - 3496
Let
X
r
=
x
r
+
y
r
+
z
r
with
x
,
y
,
z
real. It is known that if
S
1
=
0
,
(
∗
)
S
m
+
n
m
+
n
=
S
m
m
S
n
n
for
(
m
,
n
)
=
(
2
,
3
)
,
(
3
,
2
)
,
(
2
,
5
)
, or
(
5
,
2
)
. Determine all other pairs of integers
(
m
,
n
)
if any, so that
(
∗
)
holds for all real numbers
x
,
y
,
z
such that
x
+
y
+
z
=
0
.
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