The mod k chromatic index of graphs is O(k)

Let chi(k)'(G) denote the minimum number of colors needed to color the edges of a graph G in a way that the subgraph spanned by the edges of each color has all degrees congruent to 1 (mod k). Scott proved that chi(k)'(G) <= 5k(2) log k, and thus settled a question of Pyber, who had asked whether chi(k)'(G) can be bounded solely as a function of k. We prove that chi(k)'(G) = O(k), answering affirmatively a question of Scott.