There are \(n\) fish numbered \(1\) through \(n\) at one end of an aquarium. They all start swimming at the same time to the other end of the aquarium. Once a fish reaches an end of the aquarium, it turns around immediately and continues swimming in the other direction.

Fish \(1\) swims with speed \(v_1\), fish \(2\) swims with speed \(v_2 = 2 v_1\), fish \(3\) swims with speed \( v_3 = 2 v_2 \), and so on.

Will the \(n\) fish all be at the same end of the aquarium at the same time again?

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