  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 $1 \pmod k$. Scott [{\em Discrete Math.
175}, 1-3 (1997), 289--291] proved that $\chi'_k(G)\leq5k^2\log k$, and thus
settled a question of Pyber [{\em Sets, graphs and numbers} (1992), pp.
583--610], 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.
