AIME I 2010 #8

[stupidityismygam]

For a real number [unparseable or potentially dangerous latex formula], let [unparseable or potentially dangerous latex formula] denominate the greatest integer less than or equal to [unparseable or potentially dangerous latex formula]. Let [unparseable or potentially dangerous latex formula] denote the region in the coordinate plane consisting of the points [unparseable or potentially dangerous latex formula] such that [unparseable or potentially dangerous latex formula] The region [unparseable or potentially dangerous latex formula] is completely contained in a disk of radius [unparseable or potentially dangerous latex formula] (a disk is the union of a circle and its interior). The minimum value of [unparseable or potentially dangerous latex formula] can be written as [unparseable or potentially dangerous latex formula], where [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] are integers and [unparseable or potentially dangerous latex formula] is not divisible by the square of any prime. Find [unparseable or potentially dangerous latex formula].

[88bobcat]

[stupidityismygam]

Watch out, the disk is not centered at the origin.

[88bobcat]

[88bobcat]