(In reply to

'generated' by Jer)

**re Jer** Your solution would include all series with positive integers each below 520, and a<b. They would include *inter alia* **520** as a number generated by **you**, contradicting the text.

re. Steve. a=b generates a regular Fibonacci series (a=b=1) ,each number being multiplied by 520/f f being a Fibonacci number dividing 520 (520/2,520/5,520/8,520/13). I just excluded them.

Both modifications would fit an **altered text**, creating another valid puzzle.

re: All solvers-

1. One does have to list all solutions, a counting is possible like

for u(3 )=520 there are **259** solutions: u(1)=260-k, u(2)=260+k, etc

2. The 1st part of the puzzle is still open.