Number theory and set theory problem – math.stackexchange.com

Number theory and set theory problem – math.stackexchange.com

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Let $A$ be a finite set. For $0\leq i\leq 2$, let $a_i$ be the number of subsets $B$ of $A$ such that $$\#(B)\equiv i (\mathrm{mod}\,3).$$ Prove that $$|a_i - a_j| \leq 1,$$ for all $0\leq i,j\leq 2$. ...

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