Question 143
Let $\mathcal{A}$ be a nonempty set of positive integers. We say that a positive integer $n$ is *special* if there exists a unique subset $\mathcal{B}$ of the set $\mathcal{A}$ such that
(i) the number of the elements in $\mathcal{B}$ is odd;
(ii) the sum of all elements of $\mathcal{B}$ is equal to $n$.
Prove that there exist infinitely many positive integers that are not special.
(IMO-2015 Shortlist, Problem C6)
(i) the number of the elements in $\mathcal{B}$ is odd;
(ii) the sum of all elements of $\mathcal{B}$ is equal to $n$.
Prove that there exist infinitely many positive integers that are not special.
(IMO-2015 Shortlist, Problem C6)