MathDB

For a real number

a

, let

\lfloor a \rfloor

denominate the greatest integer less than or equal to

a

. Let

\mathcal{R}

denote the region in the coordinate plane consisting of points

(x,y)

such that \lfloor x \rfloor ^2 \plus{} \lfloor y \rfloor ^2 \equal{} 25. The region

\mathcal{R}

is completely contained in a disk of radius

r

(a disk is the union of a circle and its interior). The minimum value of

r

can be written as

\tfrac {\sqrt {m}}{n}

, where

m

and

n

are integers and

m

is not divisible by the square of any prime. Find m \plus{} n.

Problem Statement