TWO Proofs of Euclid's Lemma!! 🌟🌟

[@amirerfanian4418]

the second proof was really beautiful

[@sudikshaboora2529]

Very nice explanation 👍 Thanks for proof.

[@billkinneymath]

You're welcome! Thanks for watching!

[@martinsnow6010]

Euclid's lemma is a tale of commutative rings of unique primes. Madagascan lemurs are unique communal ring-tailed primates.

[@billkinneymath]

🤣

[@capybara-k6g]

thank you!!

[@billkinneymath]

You're welcome!

[@amirerfanian4418]

thank you so much Professor Kinney , if you use digital pen and paper ,it will be really great , thank you so much for your time and efforts

[@billkinneymath]

I don't have that available to me right now. Maybe I can get it this summer.

[@amirerfanian4418]

@@billkinneymath it will be really great . you know I always thinking technology can change math and programming teaching . I strongly believe math teaching is an Art and definitely you are a great artist

[@amirerfanian4418]

@@billkinneymath I strongly believe your channel can turn into a math academy .it will be my honor if I can help you about that

[@billkinneymath]

@@amirerfanian4418 Do you have resources or contacts to make that happen?

[@SanketAlekar]

For the second proof - doesn't the proof of the linear combination result use the original result you're trying to prove anyway? So it seems circular

[@billkinneymath]

You can prove the linear combination result with the Well-Ordering Principle and the Division Algorithm. No need for Euclid's Lemma.

[@SanketAlekar]

Sorry, you're right. I made a mistake in my earlier comment. I meant to say - if you use the fundamental theorem of arithmetic (not the second proof), that uses the result you are currently proving. At the step where you show that the prime factorization is unique.

[@DAIZHUOYANGHCI]

It's just Bezout's theorem