Mike has a magic scale, each side of which holds a positive integer. He plays the following game: each turn, he chooses a positive integer n. He then adds n to the number on the left side of the scale, and multiplies by n the number on the right side of the scale. (For example, if the turn starts with 4 on the left and 6 on the right, and Mike chooses n = 3, then the turn ends with 7 on the left and 18 on the right.) Mike wins if he can make both sides of the scale equal. Show that if the game starts with the left scale holding 17 and the right scale holding 5, then Mike can win the game in 4 or fewer turns.
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