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Putnam
2022 Putnam
B1
2022 Putnam B1
2022 Putnam B1
Source:
December 4, 2022
Putnam
Putnam 2022
Problem Statement
Suppose that
P
(
x
)
=
a
1
x
+
a
2
x
2
+
…
+
a
n
x
n
P(x)=a_1x+a_2x^2+\ldots+a_nx^n
P
(
x
)
=
a
1
x
+
a
2
x
2
+
…
+
a
n
x
n
is a polynomial with integer coefficients, with
a
1
a_1
a
1
odd. Suppose that
e
P
(
x
)
=
b
0
+
b
1
x
+
b
2
x
2
+
…
e^{P(x)}=b_0+b_1x+b_2x^2+\ldots
e
P
(
x
)
=
b
0
+
b
1
x
+
b
2
x
2
+
…
for all
x
.
x.
x
.
Prove that
b
k
b_k
b
k
is nonzero for all
k
≥
0.
k \geq 0.
k
≥
0.
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