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Putnam
1975 Putnam
A4
A4
Part of
1975 Putnam
Problems
(1)
Putnam 1975 A4
Source: Putnam 1975
2/17/2022
Let
m
>
1
m>1
m
>
1
be an odd integer. Let
n
=
2
m
n=2m
n
=
2
m
and \theta=e^{2\pi i\slash n}. Find integers
a
1
,
…
,
a
k
a_{1},\ldots,a_{k}
a
1
,
…
,
a
k
such that
∑
i
=
1
k
a
i
θ
i
=
1
1
−
θ
\sum_{i=1}^{k}a_{i}\theta^{i}=\frac{1}{1-\theta}
∑
i
=
1
k
a
i
θ
i
=
1
−
θ
1
.
Putnam
roots of unity