Question 65
Let $x_{1}, x_{2}, x_{3}, \ldots$ be a sequence of integers with the properties
- $1 = x_{1} \lt x_{2} \lt x_{3} \lt \ldots$,
- $x_{n+1} \leq 2 n$ for $n \geq 1$.
Show that for every positive integer $k$ there are two indices $i$ and $j$ with $k = x_{i} - x_{j}$.
- $1 = x_{1} \lt x_{2} \lt x_{3} \lt \ldots$,
- $x_{n+1} \leq 2 n$ for $n \geq 1$.
Show that for every positive integer $k$ there are two indices $i$ and $j$ with $k = x_{i} - x_{j}$.