Fibonacci sequence

Find the least positive integer d for which there exists an 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(1) for n>=1 ,The arithmetic progression has infinitely many terms

#NumberTheory #FibonacciNumbers

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$