Exploring Number Theory the Pythagorean Way: Right Triangles, Sums of Squares, and Arithmetic

Exploring Number Theory the Pythagorean Way: Right Triangles, Sums of Squares, and Arithmetic offers a captivating journey through elementary number theory with a Pythagorean twist. This book explores the Pythagorean theorem’s connection to diverse number theory concepts such as Fermat’s theorem, Diophantine equations, and primes of the form 4k+1. It delves into more advanced topics like quadratic reciprocity, Pythagorean triples, and counting lattice points. With an emphasis on practicality, it introduces readers to Gauss sums, the four squares theorem, and quadratic forms. Whether you’re a mathematics enthusiast or a student using SageMath, this book provides an engaging and comprehensive exploration of number theory through the lens of the Pythagorean theorem.