  We show that with high probability the random graph $G_{n, 1/2}$ has an
induced subgraph of linear size, all of whose degrees are congruent to $r\pmod
q$ for any fixed $r$ and $q\geq 2$.
  More generally, the same is true for any fixed distribution of degrees modulo
$q$.
  Finally, we show that with high probability we can partition the vertices of
$G_{n, 1/2}$ into $q+1$ parts of nearly equal size, each of which induces a
subgraph all of whose degrees are congruent to $r\pmod q$.
  Our results resolve affirmatively a conjecture of Scott, who addressed the
case $q=2$.
