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Rioplatense Mathematical Olympiad, Level 3
1997 Rioplatense Mathematical Olympiad, Level 3
1
1
Part of
1997 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
integer polynomial
Source: VI - Rioplatense 1997 L3 P1
9/19/2022
Find all positive integers
n
n
n
with the following property: there exists a polynomial
P
n
(
x
)
P_n(x)
P
n
(
x
)
of degree
n
n
n
, with integer coefficients, such that
P
n
(
0
)
=
0
P_n(0)=0
P
n
(
0
)
=
0
and
P
n
(
x
)
=
n
P_n(x)=n
P
n
(
x
)
=
n
for
n
n
n
distinct integer solutions.
polynomial
algebra