Let k be a fixed natural number. In the infinite number of real line, each integer is colored with color ..., red, green, blue, red, green, blue, ... and so on. A number of flea settles at first at integer points. On each turn, a flea will jump over the other tick so that the distance k is the original distance. Formally, we may choose 2 tails A,B that are spaced n and move A to the different side of B so the current distance is kn. Some fleas may occupy the same point because we consider the size of fleas very small. Determine all the values of k so that, whatever the initial position of the ticks, we always get a position where all ticks land on the same color. combinatoricsInteger sequence