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Putnam
2021 Putnam
A6
A6
Part of
2021 Putnam
Problems
(1)
Putnam 2021 A6
Source:
12/5/2021
Let
P
(
x
)
P(x)
P
(
x
)
be a polynomial whose coefficients are all either
0
0
0
or
1
1
1
. Suppose that
P
(
x
)
P(x)
P
(
x
)
can be written as the product of two nonconstant polynomials with integer coefficients. Does it follow that
P
(
2
)
P(2)
P
(
2
)
is a composite integer?
Putnam
Putnam 2021