# PORC function

## Definition

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.

## Facts

- 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 .