Abundances Of Absolutes
Algebra
Level
3
\[\mathcal A=\displaystyle\sum_{i=1}^{2016}\left|x-a_i\right|\]
Let \(a_1,a_2,a_3,\ldots ,a_{2016}\) form an increasing arithmetic progression (AP) which consists of only positive terms. Let the minimum value of \(\mathcal A\) be \(2016^2\) for real \(x\). Then find the sum of all possible values of the common difference of AP.
Notation: \( | \cdot | \) denotes the absolute value function.
by
Rishabh Cool