Take a set of numbers from {0,1,2,......n-1} of group Z_n
Is it possible to write a number or in the sense some number between 0 to n-1 as a sequence of operations of addition and subtraction under addition modulo n using the remaining numbers exactly once and such that also such that if like
Example : 0 = (-1) + (-2) + (+1) + (2)
(0,1) + (1,3) + (3,2) + (2,0)
conditions
Here any number should appear twice only either as a negative or positive some time both positive and both negative but the number should appear only twice.
Second condition is distance between two same numbers say (-2) and (2) or (2) and (2) or (-2) and (2) should be unique and should be the same as the distance between any other number. Here (1) has distance 2 as u can see (-2) in the middle and
(2) has distance 1. I have written these numbers too as (a,b) => (a-b) below where (a,b) 1
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