Do there exist $n$ rational numbers $a,a_2,...,a_n\;$, $n>2$, such that their difference (in order) is $0$ and their sum is $1$?
That is, are their any rational solutions $a_1,a_2,...,a_n$ to:
$a+a_2+a_3$ $=$ $1$, $a-a_2-a_3$ $=$ $0$
$a+a_2+a_3+a_4$ $=$ $1$, $a-a_2-a_3-a_4$ $=$ $0$
$a+a_2+a_3+...+a_n$ $=$ $1$, $a-a_2-a_3-...-a_n$ $=$ $0$
(The order of the numbers is important)
If not, is there a simple proof to show that the specified conditions can't be satisfied?
Thanks for help.