https://stm2.bookpi.org/NASNUM <p>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.</p> en-US Nasty Numbers https://stm2.bookpi.org/NASNUM/article/view/839 <p><strong>Aim :</strong>An interesting pattern arising out of integers known as Nasty numbers is studied for its various characterizations.</p> <p><strong>Methodology:</strong> The general forms of nasty number, double nasty number and triple nasty number are obtained by utilizing substitution technique and solutions of quadratic equation.</p> <p><strong>Results:</strong>. Patterns of polygonal numbers ,centered polygonal numbers, pyramidal numbers and centered pyramidal numbers in relation to nasty numbers are exhibited. The process of obtaining pairs of pythagorean triangles and triples of pythagorean triangles with the same area respectively has been illustrated. Characterizations of pythagorean triangles in relation to nasty numbers have been studied.</p> <p><strong>Conclusion:</strong> The authors have taken care to present various characterizations of nasty numbers in an elegant way. The researchers in this field may look for patterns and relations to other choices of numbers.</p> Dr. S. Devibala Dr. M. A. Gopalan Copyright (c) 2026 Author(s). The licensee is the publisher (BP International). 2026-01-24 2026-01-24 1 81 10.9734/bpi/mono/978-93-47485-33-6