Production Conundrum

There are two machines:

  • machine 1 which produces k+1 shoes every minute. (That is, one shoe comes out of the machine every 1/(k+1) th of a minute.)

  • machine 2 which produces k shoes every minute. (That is, one shoe comes out of the machine every 1/k th of a minute.) where k is a positive integer.

Both machines produce alternatingly right and left shoes (starting with the left shoe). They are switched on at the exact same time. When machine 1 has produced 2017 more shoes than machine 2, how often did it occur that a left shoe came out of each machine at the exact same moment?

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