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Austria Contests
Austrian MO National Competition
1988 Federal Competition For Advanced Students, P2
6
6
Part of
1988 Federal Competition For Advanced Students, P2
Problems
(1)
monic polynomials
Source: Austria 1988
7/8/2009
Determine all monic polynomials
p
(
x
)
p(x)
p
(
x
)
of fifth degree having real coefficients and the following property: Whenever
a
a
a
is a (real or complex) root of
p
(
x
)
p(x)
p
(
x
)
, then so are
1
a
\frac{1}{a}
a
1
and 1\minus{}a.
algebra
polynomial
algebra unsolved