# Is this even possible?

Algebra Level 5

For fixed integers $$n,k$$, there exists a sequence of $$n$$ terms $$x_1,x_2,x_3,\ldots,x_n$$, such that the sum of any $$k$$ distinct terms is equal to the sum of the all the other term minus the serial number of each the $$k$$ terms. After some calculations, it is found out that each term is in an arithmetic sequence, they have a common difference which is denoted by $$d(n,k)$$. Compute $d(2016,2015)+d(2015,1729).$

Details and Assumptions

As a explicit example if $$n=4,k=2$$. then

$x_\boxed{1}+x_\boxed{2}=x_3+x_4-\boxed{1}-\boxed{2}$

Extra credit: Solve for general term and also when the terms doesn't start at $$n_1$$ but at $$n_a$$ for positive integer $$a$$.

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