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Miklós Schweitzer
2015 Miklos Schweitzer
5
5
Part of
2015 Miklos Schweitzer
Problems
(1)
Composition of Polynomials
Source: Miklos Schweitzer 2015 Problem 5
11/20/2015
Let
f
(
x
)
=
x
n
+
x
n
−
1
+
⋯
+
x
+
1
f(x) = x^n+x^{n-1}+\dots+x+1
f
(
x
)
=
x
n
+
x
n
−
1
+
⋯
+
x
+
1
for an integer
n
≥
1.
n\ge 1.
n
≥
1.
For which
n
n
n
are there polynomials
g
,
h
g, h
g
,
h
with real coefficients and degrees smaller than
n
n
n
such that
f
(
x
)
=
g
(
h
(
x
)
)
.
f(x) = g(h(x)).
f
(
x
)
=
g
(
h
(
x
))
.
algebra
polynomial
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