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 2018-12-13, 14:46 #1 wildrabbitt   Jul 2014 1BF16 Posts 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.
2018-12-13, 15:15   #2
paulunderwood

Sep 2002
Database er0rr

22×859 Posts

Quote:
 Originally Posted by wildrabbitt 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

 2018-12-13, 16:15 #3 R. Gerbicz     "Robert Gerbicz" Oct 2005 Hungary 140910 Posts 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).
 2018-12-13, 16:41 #4 wildrabbitt   Jul 2014 3×149 Posts Thanks very much.

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