Question 32
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.
Show that Germán can always achieve his goal.
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.
Show that Germán can always achieve his goal.