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Putnam
1974 Putnam
B3
B3
Part of
1974 Putnam
Problems
(1)
Putnam 1974 B3
Source: Putnam 1974
5/28/2022
Prove that if
a
a
a
is a real number such that
cos
π
a
=
1
3
,
\cos \pi a= \frac{1}{3},
cos
πa
=
3
1
,
then
a
a
a
is irrational.
Putnam
irrational
cosine