Nasty Numbers

This book delves into the intriguing world of Nasty numbers, a fascinating pattern emerging from integers. We explore various characterizations of these numbers, revealing their unique properties and relationships with other mathematical concepts. Through the use of substitution techniques and solutions to quadratic equations, we derive the general forms of nasty numbers, double nasty numbers, and triple nasty numbers. Our investigation also uncovers patterns connecting nasty numbers to polygonal numbers, centered polygonal numbers, pyramidal numbers, and centered pyramidal numbers. Furthermore, we illustrate methods for generating pairs and triples of Pythagorean triangles with the same area, shedding light on the connections between nasty numbers and Pythagorean triangles. It is our hope that this work will inspire researchers to explore further patterns and relationships between nasty numbers and other areas of mathematics, leading to new discoveries and insights.