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Austria Contests
Austrian MO National Competition
2005 Federal Competition For Advanced Students, Part 2
2
(a,b,c,d,e,f)
(a,b,c,d,e,f)
Source: Austrian MO 2005 round 2
June 27, 2005
algebra unsolved
algebra
Problem Statement
Find all real
a
,
b
,
c
,
d
,
e
,
f
a,b,c,d,e,f
a
,
b
,
c
,
d
,
e
,
f
that satisfy the system
4
a
=
(
b
+
c
+
d
+
e
)
4
4a = (b + c + d + e)^4
4
a
=
(
b
+
c
+
d
+
e
)
4
4
b
=
(
c
+
d
+
e
+
f
)
4
4b = (c + d + e + f)^4
4
b
=
(
c
+
d
+
e
+
f
)
4
4
c
=
(
d
+
e
+
f
+
a
)
4
4c = (d + e + f + a)^4
4
c
=
(
d
+
e
+
f
+
a
)
4
4
d
=
(
e
+
f
+
a
+
b
)
4
4d = (e + f + a + b)^4
4
d
=
(
e
+
f
+
a
+
b
)
4
4
e
=
(
f
+
a
+
b
+
c
)
4
4e = (f + a + b + c)^4
4
e
=
(
f
+
a
+
b
+
c
)
4
4
f
=
(
a
+
b
+
c
+
d
)
4
4f = (a + b + c + d)^4
4
f
=
(
a
+
b
+
c
+
d
)
4
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