Question 142
A flea is initially on a vertex of a regular polygon with 2015 sides; it makes a sequence of jumps counterclockwise: at the first jump it moves by one vertex (from the initial vertex to its neighbour), at the second by three, at the third by five, and so on, so that at the $n$-th jump it leaves a vertex and lands $2 n-1$ vertices further on, always counterclockwise. After how many jumps will it happen for the first time that the flea lands on a vertex it had already visited?