Date: Feb 14, 2014 4:40 PM
Author: quasi
Subject: real parts of powers
Warmup problem (not hard):

Show that there exists a complex number c such that Re(c^n)

is nonzero for all positive integers n, and such that

Re(c^n1) = Re(c^n2) = Re(c^n3)

for some distinct positive integers n1,n2,n3.

Conjecture:

There does not exist a complex number c such that Re(c^n)

is nonzero for all positive integers n, and such that

Re(c^n1) = Re(c^n2) = Re(c^n3) = Re(c^n4)

where n1,n2,n3,n4 are distinct positive integers.

quasi