# Sorry, Fibonacci.

**Number Theory**Level 4

Find the least positive integer \(d\) for which there exists an infinite arithmetic progression satisfying the following properties:

- Each term of the progression is a positive integer.
- The common difference of the progression is \(d\).
- 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.