TITLE: Does this problem have a name?  [Ducci Sequences]
QUESTION [5 upvotes]: Let $a_1, ... a_n$ be real numbers.  Consider the operation which replaces these numbers with $|a_1 - a_2|, |a_2 - a_3|, ... |a_n - a_1|$, and iterate.  Under the assumption that $a_i \in \mathbb{Z}$, the iteration is guaranteed to terminate with all of the numbers set to zero if and only if $n$ is a power of two.  A friend of mine knows how to prove this, but wants to be able to reference a source where this problem (and/or its generalization to real numbers) is mentioned, and we can't figure out what search terms to use.  Can anyone help us out?
(If someone can figure out a better title for this question, that would also be appreciated.)

REPLY [11 votes]: This is known as Ducci's problem. "Ducci map" or "Ducci sequence" as key words should let you search on most of the articles studying properties of the above map.