In an earlier post a question was left open. I will repeat the question here.
You start with $n$ integers $a_1, a_2, \dots, a_n$ and in one step you perform the following transformation
$$(a_1, a_2, \dots , a_n) \to (|a_1-a_2|, |a_2 - a_3|, \dots, |a_{n-1} - a_n|, |a_n - a_1|)$$
($|x| = $ absolute value of $x$)
You keep performing this operation till all the numbers become zero.
Find all $n \gt 1$ (with proof), such that no matter which integers you start with, the numbers eventually become zero.
You start with $n$ integers $a_1, a_2, \dots, a_n$ and in one step you perform the following transformation
$$(a_1, a_2, \dots , a_n) \to (|a_1-a_2|, |a_2 - a_3|, \dots, |a_{n-1} - a_n|, |a_n - a_1|)$$
($|x| = $ absolute value of $x$)
You keep performing this operation till all the numbers become zero.
Find all $n \gt 1$ (with proof), such that no matter which integers you start with, the numbers eventually become zero.
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