MathDB

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=5^2+2^3

. 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.

Problem Statement