Decide whether there exists a set
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
of positive integers satisfying the following conditions:
(i) For any natural numberm
![>1](/media/m/b/8/a/b8a19fa83da7eca60bb9ecc5d63b7d8e.png)
there are
![a, b \in M](/media/m/8/6/f/86fa336fb3c5fa01d4775ce530e9db8e.png)
such that
![a+b = m.](/media/m/2/5/4/2542b7af1b7fb139a05316d093f0e280.png)
(ii) If
![a, b, c, d \in M , a, b, c, d > 10](/media/m/6/4/3/6436c1dbfa74d57066915fc032f76be8.png)
and
![a + b = c + d](/media/m/5/1/a/51a108e910c5c0b684f6aab6bbfba767.png)
, then
![a = c](/media/m/9/0/5/90549bc90f177968b840f52eb6150aa2.png)
or
%V0
Decide whether there exists a set $M$ of positive integers satisfying the following conditions:
(i) For any natural numberm $>1$ 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 $a = d.$