Number Theory | Congruence and Equivalence Classes

We prove the congruence modulo n is an equivalence relation on the set of integers and describe the equivalence classes.

[@moslemasultana9388]

very nice venture. Oxygen for us, the noobs attempting to do well in olympiads.

[@georgesadler7830]

Professor Michael Penn, thank you for another awesome lecture on Congruence and Equivalence Classes in old fashion Number Theory.

[@gabrieldoria3269]

This playlist is awesome!!! I'm a Brazilian student and your lessons are wonderful!!! Congratulations on your didactic.

[@Thadnill]

Very nice biceps.. the video was also very nice!

[@pariminagalakshmi5517]

Sir , u helped me a lot by your videos ... Thank you so much....And keep going like this .. and upload many videos on maths ..as I m waiting for your videos.... Once again thank you so much

[@Abhisruta]

What textbook for number theory do you prefer? Good videos...

[@tanjinaaktar1146]

You can't imagine how much help you do for us❤

[@theunknown4209]

the sound of the chalk marks striking the board reminds me of old kung fu movies.

[@rahelina7176]

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[@maryamshafik7795]

thanks a lot!

[@PunmasterSTP]

Congruence? More like con-greatness! Thinks again for making and posting all of these wonderful explanations!

[@hadeelbi8363]

Perfect ❤️

[@mdnahidalraj_5395]

Thank so much sir

[@dimosvavaitis8653]

Hi. Thanks a lot! You are doing a grate job! You are helping me a lot to understand Number Theory. May i ask something? At 4:45 at example x=2 and n=3 the equivalence class might have 5 also? {...-4,-1,2,(5),8,11,...} cause 3|5-2?

[@dimosvavaitis8653]

Ok i am sorry. I was a bit harry. :) I should wait until the end of the video (or 23 more seconds :) ). Thanks a lot again!

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[@deuteriumtritium9700]

I think you just need to watch over 30 seconds. And yes, so will I.

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[@soulmansaul]

Did you film this in the garage?

[@NorthPoleSun]

you're big bro

[@MicaelSLopes]

não posso dizer que é muito útil...só a transcrição do que qualquer livro de álgebra abstracta diz.

[@tomnijssen8712]

Nice video, but why isn't there an equivalence class for n? Why only from 0 to n-1? Thank you! :)

[@paolo_benda]

There is an equivalence class for n! But this class is equal to the equivalence class of 0.

[@pranjaldas1762]

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He does rock climbing,diving,Olympic dead lifts and couple of other things.

[@josephquinto5812]

I’m a just-graduated senior in high school, but I’m starting to understand this I think 😂

[@JR-iu8yl]

Keep going