Talk:Divisibility sequence

Difference of Powers

"Every sequence of the form {\displaystyle a_{n}=A^{n}-B^{n}} a_n = A^n - B^n for integers {\displaystyle A>B>0} A>B>0 is a divisibility sequence."

does it have to have integer A and B? The Fibonacci and other recurrence sequences can be expressed in this form with non-integer A and B, but integer values. Walt (talk) 00:45, 14 September 2016 (UTC)

@Wroscel:, the remark about Lucas sequences provides the right generalization to non-integer values. (Any Lucas sequence has an explicit form similar to the Fibonacci numbers -- though it does not quite have this form, there is a constant factor dividing the whole sequence.) --JBL (talk) 14:43, 8 June 2017 (UTC)

I had exactly the same question. I've changed the article text to indicate the connection. —Quantling (talk | contribs) 02:57, 8 November 2025 (UTC)