MathDB

Let

n \ge 5

be an integer and let

x_1, x_2, ... , x_n

n

distinct integer numbers such that no

3

of them can be in arithmetic progression. Prove that if for all

1 \le i, j \le n

we have

2|x_i - x_j | \le n(n - 1)

then there exist

4

distinct indices

i, j, k, l \in \{1, 2, ... , n\}

such that

x_i + x_j = x_k + x_l.

5.2