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Topic: arithmetic progression that's also a geometric one, with a known largest number, need advice
Replies: 4   Last Post: Dec 5, 2012 1:11 AM

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Edwill

Posts: 1
Registered: 1/29/05
arithmetic progression that's also a geometric one, with a known largest number, need advice
Posted: Jan 25, 2005 6:00 PM
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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





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