Question 24
A grasshopper is sitting in the origin of the number line, at number $0$, and then it jumps, always in the same direction. For a positive integer $k$, in the first jump the grasshopper jumps to number $1$, and every following jump is exactly $k$ times longer than the previous jump. There is a hole in place of all multiples of number $2015$. Determine all positive integers $k$ such that the grasshopper can jump $2015$ times without falling into a hole. (Ilko Brnetić)