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National and Regional Contests
Moldova Contests
Chisinau City MO
1976 Chisinau City MO
126
126
Part of
1976 Chisinau City MO
Problems
(1)
Chisinau MO p126 1976 IX P (n + km) is divisible by m for any integer k
Source:
3/16/2021
Let
P
(
x
)
P (x)
P
(
x
)
be a polynomial with integer coefficients and
P
(
n
)
=
m
P (n) =m
P
(
n
)
=
m
for some integers
n
,
m
n, m
n
,
m
(
m
≠
10
m \ne 10
m
=
10
). Prove that
P
(
n
+
k
m
)
P (n + km)
P
(
n
+
km
)
is divisible by
m
m
m
for any integer
k
k
k
.
algebra
polynomial
divisible