Number Theory | Sums of Squares Part 1.

[@carlosdanielvelazquezflore6512]

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.

[@MichaelPennMath]

Thanks, that is great to hear.

[@ThePharphis]

You're right, the proofs were easy. Thanks

[@georgesadler7830]

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

[@idolgin776]

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.

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.

[@johnlovesmath]

This is a very high quality explanation. Thx.

[@zahraalipour3550]

tres bien!
merci beaucoup

[@ytchannel-yn3hb]

0 isn't a natural number

[@tenran3147]

Part2 will be comin.

[@MichaelPennMath]

It will be available tonight!

[@tenran3147]

Michael Penn thanks!

[@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?

[@owlsmath]

This was great! And so useful

[@preraksemwal8768]

awesome explanation

[@jakobthomsen1595]

Neat!

[@djvalentedochp]

nice

[@ayeshaqureshi9875]

0 doesn't belongs to N...

[@adarshyadav253]

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

[@hybmnzz2658]

The final result will be better

[@tomatrix7525]

Depending on definitions, 0 can be a natural no.

[@dicksonchang6647]

0 is natural number

[@Ravit14]

nice