ILL 1983 Problem 51

Decide whether there exists a set $M$ of positive integers satisfying the following conditions:

(i) For any natural number $m>1$ there exist $a, b \in M$ such that $a+b = m.$

(ii) If $a, b, c, d \in M$, $a, b, c, d > 10$ and $a + b = c + d$, then $a = c$ or $a = d.$