Question 196
Let $S$ be a set of $n \gt 1$ distinct integers and suppose that
$$
T = \{x + y : x \neq y, x, y \in S\}
$$
has exactly $2n - 3$ distinct elements. Prove that, when arranged in increasing order, the elements of $S$ form an arithmetic progression.
$$
T = \{x + y : x \neq y, x, y \in S\}
$$
has exactly $2n - 3$ distinct elements. Prove that, when arranged in increasing order, the elements of $S$ form an arithmetic progression.