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.)



Does this problem have a name?  [Ducci Sequences]
This is known as [Ducci's problem](http://en.wikipedia.org/wiki/Ducci_sequence). "Ducci map" or "Ducci sequence" as key words should let you search on most of the articles studying properties of the above map.


