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Putnam
1973 Putnam
B2
B2
Part of
1973 Putnam
Problems
(1)
Putnam 1973 B2
Source: Putnam 1973
5/25/2022
Let
z
=
x
+
y
i
z=x+yi
z
=
x
+
y
i
be a complex number with
x
x
x
and
y
y
y
rational and with
∣
z
∣
=
1.
|z|=1.
∣
z
∣
=
1.
Prove that the number
∣
z
2
n
−
1
∣
|z^{2n} -1|
∣
z
2
n
−
1∣
is rational for every integer
n
n
n
.
Putnam
complex numbers
rational number