# Chapter 20_Integer Sequences, Discriminants and the Dedekind Eta Function

In this Chapter I will discuss the complex eta function and how the eta quotient can be used to find the real solution of several irreducible cubic polynomials.  For some particular prime and negative binary quadratic discriminant, the eta quotient can be used to find primes which split the irreducible polynomial mod p. Once these primes are found all irreducible polynomials of degree 3 can be converted to integer sequences.  The magnitude of the period of these sequences is further discussed.

Integer Sequences, Discriminants and the Dedekind Eta Function_

Perrin Sequence Lengths – Originally generated by Christian Holzbaur

The period of Perrin (0,2,3,2,5,5,…, A001608) sequence mod n. A Mathematica program is found for Perrin Periods in OEIS A104217

Board20a_Perrin Sequence Lengths