We will say that a positive integer is a winner if it can be written as the sum of a perfect square plus a perfect cube. For example, 33 is a winner because 33=52+23 .
Gabriel chooses two positive integers, r and s, and Germán must find 2005 positive integers n such that for each n, the numbers r+n and s+n are winners.
Prove that Germán can always achieve his goal. number theoryperfect cubePerfect Squaregeometry3D geometry