common difference 0

wildrabbitt · 2018-12-13, 14:46

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.

paulunderwood · 2018-12-13, 15:15

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.

R. Gerbicz · 2018-12-13, 16:15

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).

wildrabbitt · 2018-12-13, 16:41

Thanks very much.

2018-12-13, 14:46	#1
wildrabbitt Jul 2014 447₁₀ 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.

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2018-12-13, 16:15	#3
R. Gerbicz "Robert Gerbicz" Oct 2005 Hungary 2714₈ 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.