Let be the region in the -plane consisting of points satisfying

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

R

be the region in the

xy

-plane consisting of points

(x,y)

satisfying

[x^2]=[y]

, where

[x]

denotes the greatest integer less than or equal to

x

. Then

R

defines (1) A parabola whose axis is horizontal (2) A parabola whose axis is vertical (3) Integer points of the parabola

y=x^2

(4) None of the above