# Sorry, Fibonacci.

Find the least positive integer $$d$$ 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 $$d$$.
3. No term of the progression appears in the Fibonacci sequence.

Details and assumptions

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

The arithmetic progression has infinitely many terms.

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