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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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Ari

Posts: 53
Registered: 1/25/05
Re: arithmetic progression that's also a geometric one, with a known largest number, need advice
Posted: Jan 27, 2005 10:34 PM
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"Edwill" <nosmapn@lamof.com> wrote in message news:ct6j3b$g3e$1@titan.btinternet.com...
> 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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A progression that is both arithmetic and geometric must be constant.


Aristotle Polonium


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