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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1994 Moldova Team Selection Test
4
4
Part of
1994 Moldova Team Selection Test
Problems
(1)
$P(x)$ has integer values for $n+1$ consecutive values of the argument
Source: Moldova TST 1994
8/8/2023
Let
P
(
x
)
P(x)
P
(
x
)
be a polynomial with at most
n
n{}
n
real coefficeints. Prove that if
P
(
x
)
P(x)
P
(
x
)
has integer values for
n
+
1
n+1
n
+
1
consecutive values of the argument, then
P
(
m
)
∈
Z
,
∀
m
∈
Z
.
P(m)\in\mathbb{Z},\forall m\in\mathbb{Z}.
P
(
m
)
∈
Z
,
∀
m
∈
Z
.
algebra
polynomial