What does a ≡ b (mod n) mean? Basic Modular Arithmetic, Congruence

Basic congruence introduction in modular arithmetic. We will go over 3 ways to interpret a ≡ b (mod n), and you will see this in a number theory or a discrete math class. Learn how to solve congruence, subscribe to ‪@blackpenredpen‬
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[@blackpenredpen]

What donuts are those?

[@AndDiracisHisProphet]

The heart attack kind of donuts.

[@blackpenredpen]

I meant to ask where they are from

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Heaven

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Look like Krispy Kreme.

[@blackpenredpen]

Kevin got it!!

[@bakirhaljevac3584]

It took you around 3 minutes to say what I needed to know, the same thing that my professor unsuccessfully tried to explain in one hour. Thank you so much

[@v-neko8074]

same

[@tristanfan4741]

so fucking dmn right

[@finghinmccarthy5021]

True

[@JuuzouRCS]

True. I am right now going through the same experience.

[@shreyas_._]

I wonder which professor took one hour for congruence 😅then for sure your whole syllabus time schedule gonna wasted..., ഒരു മയത്തിൽ ഒക്കെ ആവം കേട്ടോ ...

[@johnlara1365]

I am a senior math and CS major, I have used modulo almost as much as I’ve used pi and I have always been confused by congruency. No one has been able to explain congruency more clearly and digestible than you. Thank you!

[@dominicellis1867]

Basically you throw out the quotient and keep the remainder. It's periodic math like the roots of a trig function.

[@v-neko8074]

Some teachers in universities: 2h lecture
blacklenredpen: 6minutes

[@davidbrisbane7206]

Too right mate, plus we can repay bprp's videos as often as we like.

[@mohammedhussain6749]

He is just explaining the procedure not the theory, origins or proof

[@EulerJr_]

@@aymenchamia7470
I do, and he is 100% right.
Our lecturer is extremely smart and knowledgeable no doubt, but he just can’t explain the procedures and concepts in a simple enough way for anyone to understand.

[@rainyday4709]

30min trying to understand this congruence with my book .
And this man make me understand it just in 1:46 seconds
I wanna cry .
Why professor make life complicated whyyy ...
THANK YOU SO MUCH.
I really respect you 🙏🙏

[@user-ok3sb9fi2j]

I watch 7 videos of about 20 minutes about modular arithmetic and didn’t understand anything but your 6 minutes video made me understand. I don’t know what to say

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PLEASE MORE MODULAR ARITHMETIC! You're the best

[@blackpenredpen]

Sergio H will do!!

[@arnasvaicekauskas7693]

Why is this video 2Pi minutes long ?

[@blackpenredpen]

It's Tau

[@unoriginalusernameno999]

Burn!

[@ansper1905]

2π=6

[@sieger358]

@@ansper1905 😑😑😑3.14159265358979323846264338
...
In can not be 3😐

[@ansper1905]

@@sieger358 tell that to engineers

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Your ability to change the marker you’re writing with so fast is amazing...

[@krimzonghost1987]

I read this comment and watched the video again just because of this. lmao. Wow! You were not joking.

[@Mindmodic]

Finally I've been looking for a decent explanation for this for about an hour! Years ago when I was in school we never learned this and 'remainder' was only referred to when you were doing sums by hand, the remainder would be the next 10, 100 or 1000 etc. from your addition, I didn't see it as any other sense!

[@nithin8432]

just had a great and clear understanding this was the lecture i needed thanks a lot mate!!!

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Omg saving my grade once again. God bless you. Wish you had a patreon...

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For those of you watching this in the future:
He does!
www.patreon.com/blackpenredpen

[@yon1623]

I spent an hour trying to understand it from my book... 6 minute video is what i needed.

[@juandelacruz9125]

Thanks blackpenredpen for teaching us this!

[@WendyLee808]

Having test next week, found this video this week. Thank you 😊 Always wanted to know the interpretation of the congruent notation.

[@Ebvardh]

Lovely explanation. Helped me finally visualize this concept before you even did the examples.

[@mahadhersi3754]

Thank you professor BlackpenRedpen I appreciate you this amazing lesson.

[@WSUFan2017]

You should do more number theory, especially stuff like Euler’s totient function (since it’s my favorite subject ;D)!

[@blackpenredpen]

I will. In the meantime, you can check out Max's videos here: th-cam.com/channels/P-ZCMz7olJPUI78b_bQrvQ.htmlvideos?disable_polymer=1

[@woojason7119]

thanks for your vdo you saved me from an algorithm course
it looked me quite a long time to understand what is meant by a=b (mod n)

[@erickarbieto8111]

Eres un crack! Y todo lo digo en español, porque hasta en Latinoamerica disfrutamos de tus videos; en serio, aprendo muchísimo! Thank you!

[@azure3544]

I learned more from this guy than from my entire math class xDDD
My math teacher made this look like rocket science...

[@reahjanegalangue8343]

same hahahahahahahhaha

[@billofrights5064]

When I took abstract algebra, I found
a ≡ b (mod n) quite confusing. The meaning seems to be
a (mod n) = b (mod n), but equivalence must mean more than this.

[@vegetaiv9275]

Your explanation is amazing. It is way better than my professor's! Thank you so much!

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yoo great tutorials/lessons love ur stuff keep em coming !!

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This video was awesome! I'm so glad I found your channel. You have a new subscriber here.

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Dude i normally watch ur vids for fun but now i actually need help and i come back to ur channel😂

[@sweepingteyvat9515]

Thank you so much! This video really helps me with number theories

[@michelletan7855]

thank you so much! you are amazing to explain the modular arithmetic! thank you thank you!

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You make math so entertaining :)

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this is the best number theory explanation, well done

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Congrats on the 100k!!

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I just want to say thank you man, you really helped me out
😃

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Amazing explanation, just what I needed

[@krimzonghost1987]

C# exercises led me here... and I ain't even mad. Awesome video!

[@Isac986]

Excelente me salvaste de leer mucha álgebra, continua con el álgebra moderna que es bien interesante al igual que el calculo

[@jgz919]

Thanks for the refresher. I hardly understood this when getting my undergrad degree and now that im working on my masters it came back to haunt me 🤣

[@UnathiGX]

This is by far the best explanation....IMO!...here I come....!!!!

[@blackpenredpen]

thanks!

[@Lolnigaaaaaaaaa]

Couldn’t learn this my whole life until I saw this. Damn please complete series on modular arithmetic please sir.

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thankyou so much!! this really helped a lot 🥰🥰

[@jerrytsai9580]

Very well explained. Thank you so much.

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U made it so easy ! thanks @you

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do you have my schedule or something ?? how do you always upload what I need. thanks man !

[@blackpenredpen]

OH wow!! ; )

[@thundrking]

Straight to the point.. thanks

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Great video, loving all the number theory :)

[@blackpenredpen]

Thanks!!!

[@barence321]

In Beachy 4th Ed., the authors write " a ≡ b (mod n) if and only if n|(a - b)." The proof goes in both directions, so you see that n|(a -b) does indeed show that a/n and b/n have the same remainder. I just finished going over this proof again for my abstract algebra class. Very simple when you do the proof both ways.

[@shacharh5470]

Congruence relations and their corresponding quotient sets (and groups, and spaces, etc) are some of the richest topics in maths, and modular congruence is one of the most useful and ubiquitous ones.

[@ghassanabdalsalam9938]

thaaaaaaaaaaaaank you , amazing , I love your explanation

[@AnayBhad]

thanks for this video helped me a lot.

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Great video as always !

[@AhmedAzhad]

Thank you very much. Very well explained.

[@frankensteinapps9442]

Thanks man I was bit confused in equivalence relations when this came up , turns out I was interpreting it in a wrong way

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Thanks a lot, brief and effective

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I just keeping learning a lot from you.
Greetings from Mexico!
Can you talk about set theory or keep doing number theory?

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Silvestre Frijol Cruz thank you!! I will focus on number theory, probability and combinatorics and calc.

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Amazing video! Thank you!

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Great video, would love some more examples to cement how to use :)

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I would attend every class of this guy 😭👍💓

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Thanks a lot man. That helps a lot!

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Good video. It helped a lot. Thanks!

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Thank you for explaining this in a straightforward manner, I FUCKING LOVE YOU!

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great teaching🥰 I finally understand 👍

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u are the best professor..

[@elijahseh7112]

Can you please do a video on multiplicative inverse modular arithmetic? I fully understand the basic modular arithmetic but finding the multiplicative inverse in modular arithmetic just keeps going over my head!

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No one told me this! And neither I could understand anyone but now I can

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You are great.
Thank You Very Much

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thanks this helped me pass my test

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Very helpful! Thanks!!

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Excellent explanation!

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Thanks that was helpful to me.

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It was very helpful.Nice video.Keep uploading more videos.....

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Crystal clear!

[@itzmrinyy7484]

Thank you so mucj for this video! I was just watching an IMO prpblem solving video and i couldn't help but wonder what "mod(n)" meant.

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This is really helpful! Where is the number Theory section in your channel

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Helpful man thanks ; )

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Wow I wish I found this in my first year. It would've saved me hours of lengthy abstract examples and confusion. Why do universities make things so unnecessarily complicated sometimes 🙄.

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U just explained a concept which my maths tutor took 35 minutes to explain in under 10 minutes.
Kudos to you sir!!

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THANK YOU SO MUCH!

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excellent explanation

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Thank you!

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Thank you for this!! :DD

[@blackpenredpen]

: )

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thank you mr. pen

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Thank you for this video

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: D this is exactly what I taught my students.

[@blackpenredpen]

: )))))

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Thank you very much

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Smooth explanation

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very good video and very good explanation!

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that was so good. thanks

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Eightc yup!!!!

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And max, you can record an intro and send it to me via google drive so I can put it in my videos to let more ppl know about ur channel.

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blackpenredpen thanks!!

[@alexcalabro8140]

Very good, thank you!

[@roof310]

(by wikipaedia) Actually, the first claim is the most correct one, same remainder when a and b are divided by n,
a = kn + r, b = jn + r then we have a - b = (k-j)n + 0 which means that n | a - b (the last claim). If we add b to both side,
a = Kn + b by setting K = k - j.
edit: depends on variables to choose the most suitable one.

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bro you really came through i was having trouble understanding that claim

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THANK YOU!

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Please keep uploading Number Theory videos!

[@blackpenredpen]

ok!!!!!!!!

[@GeorgeDCowley]

Thanks for telling me that the brackets were important.
I was just subtracting.

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Great video!

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Thank you😊

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This video has the most epic donut-math intro to be honest.