Question 4
Let $a,b$ be positive integers and $A,B$ finite sets of integers such that:
(i) $A$ and $B$ are disjoint;
(ii) if $i\in A\cup B$, then $i+a\in A$ or $i-b\in B$.
Prove $a|A|=b|B|$, where $|X|$ is the number of elements of $X$.
(i) $A$ and $B$ are disjoint;
(ii) if $i\in A\cup B$, then $i+a\in A$ or $i-b\in B$.
Prove $a|A|=b|B|$, where $|X|$ is the number of elements of $X$.