TWO Proofs of Euclid's Lemma!! 🌟🌟
Euclid's Lemma says that if p is a prime and p divides the product ab (p|a*b), then p divides a or p divides b (p|a or p|b). I prove Euclid's Lemma two ways, using: 1) Fundamental Theorem of Arithmetic, 2) GCD is a Linear Combination Theorem. "Friendly Introduction to Number Theory": https://amzn.to/3Ixo9Lq 🔴 Abstract Algebra Course Lectures playlist: • Abstract (Modern) Algebra Course Lectures 🔴 "Ultimate AP Calculus AB Review": • Ultimate AP Calculus AB Review #eucliddivisionlemma #euclidlemma #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 (0:25) Necessity of p being prime (0:57) Proof 1 (use Fundamental Theorem of Arithmetic and a proof by contrapositive) (4:24) Proof 2 (use GCD is a Linear Combination Theorem and a direct proof) AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.
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