MathDB

The graph of

{(x^2 + y^2 - 1)}^3 = x^2 y^3

is a heart-shaped curve, shown in the figure below. [asy] import graph; unitsize(10); real f(real x) { return sqrt(cbrt(x^4) - 4 x^2 + 4); } real g(real x) { return (cbrt(x^2) + f(x))/2; } real h(real x) { return (cbrt(x^2) - f(x)) / 2; } real xmax = 1.139028; draw(graph(g, -xmax, xmax) -- reverse(graph(h, -xmax, xmax)) -- cycle); xaxis("

x

", -1.5, 1.5, above = true); yaxis("

y

", -1.5, 1.5, above = true); [/asy] For how many ordered pairs of integers

(x, y)

is the point

(x, y)

inside or on this curve?

Problem Statement