Date: Jan 25, 2005 6:00 PM
Author: Edwill
Subject: arithmetic progression that's also a geometric one, with a known largest number, need advice

Hi all,

The problem is that an arithmetic progression (a_1,...,a_n), is also a
geometric progression (after applying some permutation). They (a_i's) are
all different, and the largest number of them is 2004.

Any idea to begin with to make a breakthrough?

So far,

1). they have the same sum
2). the series is either monotonic increasing, or decreasing
3). if 2). is the case, and without loss of generality, can i assume
a_n=2004. or am i already lost in 2).?

Thank you very much...I just need some enlightening hint...:D