Question 15
(POL 3) Decide whether there exists a set $M$ of natural numbers satisfying the following conditions:
(i) For any natural number $m>1$ there are $a,b\in M$ 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 $a=d$.
(i) For any natural number $m>1$ there are $a,b\in M$ 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 $a=d$.