Number Theory Through the Eyes of Sophie Germain

David Pengelley, Oregon State University, Corvallis, OR.

• IntroductionSophie Germain, number theory, and Fermat's last theoremGermain's plan to prove Fermat's last theoremFermat's last theorem for exponent fourGermain's grand plan and a letter to GaussCongruence, Germain's basic lemma, systems of linear congruences, and higher power congruencesPrimitive rootsGermain carrying out her grand planLarge size of solutions and Sophie Germain's theoremThe demise of the grand plan: A letter to LegendrePrime patterns in quadratic formsHow Fermat discovered his theorem, and other divisibility delightsBibliographyCreditsIndex

“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Germain is simultaneously a masterpiece of historical scholarship, a guide to reading and teaching from primary-source historical documents, an inquiry-based textbook for introductory number theory, and the riveting story of a major, but still unappreciated, mathematician.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