Question 15
A grasshopper moves in the plane. From a point $(x,y)$, it may jump either to $(x+y,y)$ or to $(x,x+y)$. It started at $(n,9)$, where $n$ is a positive integer, but does not remember the value of $n$. It knows only that after some number of moves it reached $(2021,2050)$. How many values of $n$ are possible?