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Video Source: www.youtube.com/watch?v=z8XLFj8MeVw
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 Lect... • 🔴 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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