Originally posted by AgergTake it to Posers and Puzzles, Spanky.
Let B be the boycott operator applied to a poster p_i, with B^2(p_i) = B(B(p_i)) denoting the boycott operator applied to the boycotter of p_i. Let n be a positive integer, and 0 be the empty boycott. Then there exists k such that for all n > k, B^n(p_i) = 0.
Proof left as an exercise for the reader.