MathDB

Putnam 1950 A6

Source:

May 24, 2022

Putnam

Problem Statement

Each coefficient

a_n

of the power series

a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \cdots = f(x)

has either the value of

f(x)

or the value

0.

Prove the easier of the two assertions:
(i) If

f(0.5)

is a rational number,

f(x)

is a rational function.
(ii) If

f(0.5)

is not a rational number,

f(x)

is not a rational function.

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