Bezout's Lemma | Road to RSA Cryptography #2

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This is the second video in a series of videos that leads up to the math of RSA Cryptography. This video series will cover the contents of the book "Number Theory Towards RSA Cryptography in 10 Undergraduate Lectures" available here:

This content is covered in a Discrete Math course I often teach, and is usually covered in a stand alone Number Theory course at other institutions.

In this video we cover Bezout's Lemma and a characterization of the GCD in terms of integer combinations. We will use this to prove an interesting divisibility property and end with a surprise bonus feature.

#EuclideanAlgorithm #GreatestCommonDivisor #GreatestCommonFactor

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Kicking in the putnam problem is very creative and fun. Thank you professor

anhquocnguyen

Very good introduction to Bezout’s lemma. Thank you for this: I was wondering how one could prove the generalization of Bezout’s lemma to n integers in Z. Assume a1, a2, ..., an are n integers in Z and assume their gcd is equal to d. How can we then prove that there are n integers in Z: z1, z2, ..., zn such that:
a1.z1 + a2.z2 + ... + an.zn = d.
Thank you!

marcfreydefont

Euclid's Algorithm always give us the gcd of two integers a and b and the reverse process of the algorithm does give the gcd as a linear combination of a and b. What then is the difference between Bezout's Lemma and this reverse process?

beanhwak

I like prime factorization better. It's much cooler imo but Bezout's Lemma is a lot easier to work with.

thedoublehelix

I really liked the end, beating a Putnam question in such a simple way... Of course the nontrivial part is to remember the gcd characterization haha

geometrydashmega

Bezout's Lemma | Road to RSA Cryptography #2

Bezout's Lemma | Road to RSA Cryptography #2

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