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Putnam
1952 Putnam
A1
Putnam 1952 A1
Putnam 1952 A1
Source:
May 29, 2022
Putnam
Problem Statement
Let
f
(
x
)
=
∑
i
=
0
i
=
n
a
i
x
n
−
i
f(x) = \sum_{i=0}^{i=n} a_i x^{n - i}
f
(
x
)
=
i
=
0
∑
i
=
n
a
i
x
n
−
i
be a polynomial of degree
n
n
n
with integral coefficients. If
a
0
,
a
n
,
a_0, a_n,
a
0
,
a
n
,
and
f
(
1
)
f(1)
f
(
1
)
are odd, prove that
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
has no rational roots.
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