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Extended Euclidean Algorithm: GCD is 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?:    • Euclidean Algorithm to Find the GCD o...   🔴 Abstract Algebra Course Lectures playlist:    • Abstract (Modern) Algebra Course Lect...   🔴 "Ultimate AP Calculus AB Review":    • Ultimate AP Calculus AB Review   #number #numbers #NumberTheory Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter:   / billkinneymath   🔴 Follow me on Instagram:   / 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.