Number Theory | Sums of Squares Part 1.

This is the first in a series of videos where we establish which natural numbers are expressible as the sum of two squares.

[carlosdanielvelazquezflore]

You're a great educator, sooner or later you will get the recognition you deserve Michael!

[SuperMtheory]

Great video! I'm glad I found your channel.

I have no idea what you're talking about but i figured out that the lenght of a line between any two points on a checkered notebook is a sum of two squares. All sums of two squares can be presented as such a line. Also 325 is the smallest number which can be presented in three ways as a sum of two squares.

[ThePharphis]

You're right, the proofs were easy. Thanks

[georgesadler]

Professor Penn, thank you for another great Number Theory proof. This proof is very easy to follow from start to finish.

[idolgin]

I really like patterns that come out of sums and differences of squares, and their relationship with the Pythagorean theorem in 2 or more dimensions.

[CabbagesandCondoms]

Loved the video but I'm trying to prove/disprove 2(x^2 + y^2) can be written as the sum of two squares... any help where to start?

[johnlovesmath]

This is a very high quality explanation. Thx.

[adarshyadav]

Wrong x, y belongs to N then why did u use 0 ?