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Putnam
2017 Putnam
B3
Putnam 2017 B3
Putnam 2017 B3
Source: Putnam
December 3, 2017
Putnam
Putnam 2017
Problem Statement
Suppose that
f
(
x
)
=
∑
i
=
0
∞
c
i
x
i
f(x) = \sum_{i=0}^\infty c_ix^i
f
(
x
)
=
i
=
0
∑
∞
c
i
x
i
is a power series for which each coefficient
c
i
c_i
c
i
is
0
0
0
or
1
1
1
. Show that if
f
(
2
/
3
)
=
3
/
2
f(2/3) = 3/2
f
(
2/3
)
=
3/2
, then
f
(
1
/
2
)
f(1/2)
f
(
1/2
)
must be irrational.
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