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International Contests
IMO Longlists
1979 IMO Longlists
42
42
Part of
1979 IMO Longlists
Problems
(1)
Existence of f(x) such that f(g(x))=g(f(x)).
Source: ILL 1979-42
6/2/2011
Let a quadratic polynomial
g
(
x
)
=
a
x
2
+
b
x
+
c
g(x) = ax^2 + bx + c
g
(
x
)
=
a
x
2
+
b
x
+
c
be given and an integer
n
≥
1
n \ge 1
n
≥
1
. Prove that there exists at most one polynomial
f
(
x
)
f(x)
f
(
x
)
of
n
n
n
th degree such that
f
(
g
(
x
)
)
=
g
(
f
(
x
)
)
.
f(g(x)) = g(f(x)).
f
(
g
(
x
))
=
g
(
f
(
x
))
.
quadratics
algebra
polynomial
algebra unsolved