Fibonacci Numbers and Integer Structure: Foundations for a Modern Quadrivium

In the study of integers over many centuries, simple but very useful data have often been overlooked or at least sparingly used. The development of modular rings provides a means to shed light on such data. A modular ring is effectively an array of integers which can be uniquely identified by columns and rows with the aid of linear equations. Thus the modular ring Z4 has 4 columns (or classes), an...