MathNet 2006 — Part 03 Question 119

Let $M = \{1, 2, \dots, 19\}$ and $A = \{a_1, a_2, \dots, a_k\} \subseteq M$. Find the minimum value of $k$ so that there exist $a_i, a_j \in A$ such that if $b \in M$, then $a_i = b$ or $a_i \pm a_j = b$.