Patterns in Prime Numbers: The Quadratic Reciprocity Law

Abstract

The ancient Greek philosopher Empedocles (c. 495-c. 435 b.c.e.) postulated that all known substances are composed of four basic elements: air, earth, .re, and water. Leucippus (.fth century b.c.e.) thought that these four were indecomposable. And Aristotle (384-322 b.c.e.) introduced four properties that characterize, in various combinations, these four elements: for example, .re possessed dryness and heat.