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Moscow Mathematical Olympiad
1941 Moscow Mathematical Olympiad
077
077
Part of
1941 Moscow Mathematical Olympiad
Problems
(1)
MMO 077 Moscow MO 1941 integer P(x), with odd values at 0,1, no integer roots
Source:
7/18/2019
A polynomial
P
(
x
)
P(x)
P
(
x
)
with integer coefficients takes odd values at
x
=
0
x = 0
x
=
0
and
x
=
1
x = 1
x
=
1
. Prove that
P
(
x
)
P(x)
P
(
x
)
has no integer roots.
integer roots
Integer Polynomial
polynomial
algebra