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Old 2018-12-13, 14:46   #1
wildrabbitt
 
Jul 2014

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Default common difference 0

Does anyone know if

a sequence with just one positive integer (repeated ad infinitum) is an arithmetic progression

or similarly

a sequence of finite length containing just one positive integer is an arithmetic progression?

I'm thinking about

https://en.wikipedia.org/wiki/Erd%C5...c_progressions



and it looks like a significant part of the problem.
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Old 2018-12-13, 15:15   #2
paulunderwood
 
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Database er0rr

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Quote:
Originally Posted by wildrabbitt View Post
Does anyone know if

a sequence with just one positive integer (repeated ad infinitum) is an arithmetic progression

or similarly

a sequence of finite length containing just one positive integer is an arithmetic progression?

I'm thinking about

https://en.wikipedia.org/wiki/Erd%C5...c_progressions



and it looks like a significant part of the problem.
I think an AP can have a common difference of 0, and a finite one must have at least 2 terms for the difference to well defined.

Last fiddled with by paulunderwood on 2018-12-13 at 15:16
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Old 2018-12-13, 16:15   #3
R. Gerbicz
 
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"Robert Gerbicz"
Oct 2005
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In the conjecture A is a set, so you can't use the same number multiple times. But you can ask the same conjecture for multiset, however that would be an equivalent problem (both of them are true, or false).
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Old 2018-12-13, 16:41   #4
wildrabbitt
 
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Thanks very much.
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