In a 2008 paper, Hausel and Rodriguez-Villegas studied the moduli space of (twisted) local systems on a Riemann surfaces by computing the number of representations of the fundamental group in GL_n(q). We will discuss some situations where instead of a Riemann surface, one considers an abelian variety defined over an algebraically closed field of characteristic p. For a supersingular abelian variety A, we count the number of representations of the etale fundamental group of A to GL_n(q), where q is a power of p. This count (for fixed n) turns out to be a polynomial in q. The space of such representations turns out to be a constructible set. We give an explicit formula for this polynomial, then state a few theorems which elucidate its features. In particular, we state a new result which generalizes to cosets a theorem of Frobenius about the number of solutions to x^n=1 in a finite group.