Question 6
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.
What is the smallest positive integer $d$ for which this is possible?
(The Fibonacci sequence is defined as $F_1=1$, $F_2=1$, $F_{n+2}=F_n+F_{n+1}$ for $n\ge1$.)
Paper instruction: Give a full solution, subject to the example-or-proof instructions in the question.
- 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.
What is the smallest positive integer $d$ for which this is possible?
(The Fibonacci sequence is defined as $F_1=1$, $F_2=1$, $F_{n+2}=F_n+F_{n+1}$ for $n\ge1$.)
Paper instruction: Give a full solution, subject to the example-or-proof instructions in the question.