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 F1=1,F2=1 and Fn+2=Fn+1+Fn for n≥1.
The arithmetic progression has infinitely many terms.