The statement is:
Let $A=\{(a_s(n_s)\}^k_{s=1}$ be an exact cover of $\mathbb{Z}$ with $1
The only proof I could find was here. But I have some difficulties understanding it. It is very short and it goes like this:
Without loss of generality we assume that $0\leq a_s
What I don't get is the following: $$\sum_{s=1}^k\sum_{q=0}^\infty z^{a_s+qn_s}=\sum_{n=0}^\infty z^n.$$ It just doesn't make sense to me. So what am I misunderstanding?