KZ-MO 2008 Problem 4

Find all integer solutions $(a_1,a_2,\dots,a_{2008})$ of the following equation:

$(2008-a_1)^2+(a_1-a_2)^2+\dots+(a_{2007}-a_{2008})^2+a_{2008}^2=2008$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.