The $c_2$ invariant is an arithmetic graph invariant related to quantum field
theory. We give a relation modulo $p$ between the $c_2$ invariant at $p$ and
the $c_2$ invariant at $p^s$, providing evidence for a conjecture of Schnetz.
The key result is a relation modulo $p$ between certain coefficients of powers
of products of particularly nice polynomials.Comment: 16 pages, edits according to referee comments including extracting
  the main result at the level of polynomial