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Contests
National and Regional Contests
India Contests
India National Olympiad
1992 India National Olympiad
6
6
Part of
1992 India National Olympiad
Problems
(1)
Integral functional eqn
Source: INMO 1992 Problem 6
10/4/2005
Let
f
(
x
)
f(x)
f
(
x
)
be a polynomial in
x
x
x
with integer coefficients and suppose that for five distinct integers
a
1
,
…
,
a
5
a_1, \ldots, a_5
a
1
,
…
,
a
5
one has
f
(
a
1
)
=
f
(
a
2
)
=
…
=
f
(
a
5
)
=
2
f(a_1) = f(a_2) = \ldots = f(a_5) = 2
f
(
a
1
)
=
f
(
a
2
)
=
…
=
f
(
a
5
)
=
2
. Show that there does not exist an integer
b
b
b
such that
f
(
b
)
=
9
f(b) = 9
f
(
b
)
=
9
.
calculus
integration
algebra
polynomial