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IberoAmerican
2019 IberoAmerican
2
2
Part of
2019 IberoAmerican
Problems
(1)
2019 Iberoamerican Mathematical Olympiad, P2
Source:
9/15/2019
Determine all polynomials
P
(
x
)
P(x)
P
(
x
)
with degree
n
≥
1
n\geq 1
n
≥
1
and integer coefficients so that for every real number
x
x
x
the following condition is satisfied
P
(
x
)
=
(
x
−
P
(
0
)
)
(
x
−
P
(
1
)
)
(
x
−
P
(
2
)
)
⋯
(
x
−
P
(
n
−
1
)
)
P(x)=(x-P(0))(x-P(1))(x-P(2))\cdots (x-P(n-1))
P
(
x
)
=
(
x
−
P
(
0
))
(
x
−
P
(
1
))
(
x
−
P
(
2
))
⋯
(
x
−
P
(
n
−
1
))
algebra
polynomial
Ibero-American