Area of Second Smallest Square

Number Theory Level 5

Let \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\), and \((x_4,y_4)\) be four distinct integer solutions to the equation


such that when connected, they form a square.

If this square is the second smallest possible square that can be made, then find the area of this square.

Details and Assumptions

The smallest square possible is made by the four solutions \((\pm 1, \pm 1)\). This square has area \(4\).


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