A function on an infinite subset of the natural numbers is termed a Polynomial On Residue Classes function or PORC function if there exists a natural number and polynomials such that if with and , then .
In other words, the function behaves like a polynomial on each of the residue classes modulo .
PORC functions are also called quasipolynomials, though that term has many other meanings in other contexts.
- Higman's PORC conjecture: For a fixed natural number , define for a prime as the number of isomorphism groups of order . Higman conjectured that for any fixed , is a PORC function of .