Sorry, Fibonacci.

Find the least positive integer dd for which there exists an infinite arithmetic progression satisfying the following properties:

  1. Each term of the progression is a positive integer.
  2. The common difference of the progression is dd.
  3. No term of the progression appears in the Fibonacci sequence.

Details and assumptions

The Fibonacci sequence is defined by F1=1,F2=1F_1 = 1, F_2 = 1 and Fn+2=Fn+1+Fn F_{n+2} = F_{n+1} + F_{n} for n1 n \geq 1 .

The arithmetic progression has infinitely many terms.

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