Number Theory Through the Eyes of Sophie Germain

David Pengelley, Oregon State University, Corvallis, OR.

Introduction Sophie Germain, number theory, and Fermat's last theorem Germain's plan to prove Fermat's last theorem Fermat's last theorem for exponent four Germain's grand plan and a letter to Gauss Congruence, Germain's basic lemma, systems of linear congruences, and higher power congruences Primitive roots Germain carrying out her grand plan Large size of solutions and Sophie Germain's theorem The demise of the grand plan: A letter to Legendre Prime patterns in quadratic forms How Fermat discovered his theorem, and other divisibility delights Bibliography Credits Index

"Number Theory Through the Eyes of Sophie Germain is simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primary-source historical documents, an inquiry-based textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician. Work is required of the reader. Readers are carefully guided to discover and prove almost all results for themselves in a sequence of scaffolded exploratory tasks with hints, fully integrated with the narrative. The difficulty of the inquiry tasks varies considerably, but the author provides the reader with appropriately helpful guidance at every step. An introductory number theory course taught with this text would be a remarkable, potentially life-changing, experience." - Stephen Kennedy, Carleton College and MAA Press