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

[URL]https://en.wikipedia.org/wiki/Erd%C5%91s_conjecture_on_arithmetic_progressions[/URL]



and it looks like a significant part of the problem.

[QUOTE=wildrabbitt;502609]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

[URL]https://en.wikipedia.org/wiki/Erd%C5%91s_conjecture_on_arithmetic_progressions[/URL]



and it looks like a significant part of the problem.[/QUOTE]

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.

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).

Thanks very much.