On subgraphs with degrees of prescribed residues in the random graph

We show that with high probability the random graph (Figure presented.) has an induced subgraph of linear size, all of whose degrees are congruent to (Figure presented.) for any fixed (Figure presented.) and (Figure presented.). More generally, the same is true for any fixed distribution of degrees modulo (Figure presented.). Finally, we show that with high probability we can partition the vertices of (Figure presented.) into (Figure presented.) parts of nearly equal size, each of which induces a subgraph all of whose degrees are congruent to (Figure presented.). Our results resolve affirmatively a conjecture of Scott, who addressed the case (Figure presented.).