Theory of numbers: Linear Diophantine equations

This lecture is part of an online undergraduate course on the theory of numbers.

We show how to use Euclid's algorithm to solve linear Diophantine equations. As a variation, we discuss the problem of solving equations in non-negative integers. We also show how to solve systems of linear Diophantine equations.

[Suav]

Complexity of all these lectures tends to grow exponentially from start to end. This is something I like about them. There is other method in use too, where audience is made to jump some hoops first. I find the former approach both more agreeable and didactically justified. In this sense the lessons seem to be less curricular and more open. Thank you.

[shubhmishra]

Thanks Sir!🙏🏼 No amount of appreciation is sufficient for your excellent service!

[julesjacobs]

These lectures are amazing. Everything is so well motivated and interesting and well explained. Thank you so much for posting them!

[calebparikh]

Enjoying these videos! Does anyone have any suggestions for problem sheets outside of the textbooks that were recommended?

[suupk]

Do you have any plans to do a series on orthogonal polynomials?

[MathinD]

The process used in the last example seems a bit cumbersome. A three step Gaussian elimination would have been more lucid.

[noahtaul]

Why do column operations on that last example? You’re just making solving for x and y hard for yourself. If you just use row operations, you can put it into echelon form and immediately have x and y in terms of z. Row operations are useful for the classification of finitely generated abelian groups because you don’t care about the generators themselves, you’re just trying to reduce the complexity of the relations between them, but here we do care about x, y, and z.