Extended Euclidean Algorithm: Expressing GCD as a Linear Combination

The extended Euclidean Algorithm reverses the steps to write the greatest common divisor (GCD) as a linear combination of the original whole numbers. It has many applications in number theory and abstract algebra. "Friendly Introduction to Number Theory": https://amzn.to/3Ixo9Lq 🔴 Euclidean Algorithm to Find the GCD of Two Numbers | Why Does It Work?: https://www.youtube.com/watch?v=YKC5Kw5p4Bg 🔴 Abstract Algebra Course Lectures playlist: https://www.youtube.com/playlist?list=PLmU0FIlJY-Mn3Pt-r5zQ_-Ar8mAnBZTf2 🔴 "Ultimate AP Calculus AB Review": https://www.youtube.com/playlist?list=PLmU0FIlJY-Ml4Ha5USN0kSt4TyvamTJar #number #numbers #NumberTheory Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinneymath?sub_confirmation=1 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter: https://twitter.com/billkinneymath 🔴 Follow me on Instagram: https://www.instagram.com/billkinneymath/ 🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ (0:00) Introduction (0:13) Problem statement (0:33) Euclidean Algorithm (1:35) Extended Euclidean Algorithm AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.