MathDB
Integer Area in bounded by inequalities

Source: 2015 AIME I Problem 14

March 20, 2015
geometryanalytic geometryinequalities

Problem Statement

For each integer n≥2n \ge 2, let A(n)A(n) be the area of the region in the coordinate plane defined by the inequalities 1≤x≤n1\le x \le n and 0≤y≤x⌊x⌋0\le y \le x \left\lfloor \sqrt x \right\rfloor, where ⌊x⌋\left\lfloor \sqrt x \right\rfloor is the greatest integer not exceeding x\sqrt x. Find the number of values of nn with 2≤n≤10002\le n \le 1000 for which A(n)A(n) is an integer.
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