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]

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The heart attack kind of donuts.

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I meant to ask where they are from

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Heaven

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Look like Krispy Kreme.

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Kevin got it!!

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

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[@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.

[@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.

[@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 🙏🙏

[@sergioh5515]

PLEASE MORE MODULAR ARITHMETIC! You're the best

[@blackpenredpen]

Sergio H will do!!

[@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

[@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

[@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!

[@meccamiles7816]

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.

[@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...

[@Wannabesage336]

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

[@WendyLee808]

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

[@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: czcams.com/channels/P-ZCMz7olJPUI78b_bQrvQ.htmlvideos?disable_polymer=1

[@juandelacruz9125]

Thanks blackpenredpen for teaching us this!

[@Ebvardh]

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

[@erickarbieto8111]

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

[@mahadhersi3754]

Thank you professor BlackpenRedpen I appreciate you this amazing lesson.

[@yon1623]

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

[@aaronvr_]

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

[@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.

[@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

[@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)

[@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.

[@sweepingteyvat9515]

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

[@Isac986]

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

[@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.

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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😂

[@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 :)

[@shady153]

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

[@vegetaiv9275]

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

[@krimzonghost1987]

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

[@faizzailan5936]

this is the best number theory explanation, well done

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Amazing explanation, just what I needed

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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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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 !

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OH wow!! ; )

[@jerrytsai9580]

Very well explained. Thank you so much.

[@UnathiGX]

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

[@blackpenredpen]

thanks!

[@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 🤣

[@tcpudp1429]

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

[@Ethan-mj6wy]

Great video, loving all the number theory :)

[@blackpenredpen]

Thanks!!!

[@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.

[@nirmaljyotieducationclasse9965]

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

[@zellpeppers8181]

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

[@thugpoet1847]

Amazing video! Thank you!

[@Lolnigaaaaaaaaa]

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

[@AhmedAzhad]

Thank you very much. Very well explained.

[@thundrking]

Straight to the point.. thanks

[@kaninma7237]

Good video. It helped a lot. Thanks!

[@marnierogers3931]

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

[@antoinelunaire9462]

Thanks a lot, brief and effective

[@frankensteinapps9442]

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

[@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!

[@MathsOnlineVideos]

Thanks a lot man. That helps a lot!

[@ghassanabdalsalam9938]

thaaaaaaaaaaaaank you , amazing , I love your explanation

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Great video as always !

[@AnayBhad]

thanks for this video helped me a lot.

[@BentHestad]

Very helpful! Thanks!!

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great teaching🥰 I finally understand 👍

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

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Thanks a ton, man! 👌👌

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Thanks that was helpful to me.

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I would attend every class of this guy 😭👍💓

[@nikhilgupta6415]

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

[@scar6073]

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

[@Gold161803]

I have actually seen (mod 1) used. It was to denote the fractional part of a non-integer, but non-integers aren't being considered here

[@robertkissinger6050]

Excellent explanation!

[@utkarshraj3272]

You are great.
Thank You Very Much

[@bgbg418]

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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Helpful man thanks ; )

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Thank you for this!! :DD

[@blackpenredpen]

: )

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u are the best professor..

[@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.

[@thimirabandara679]

very good video and very good explanation!

[@valentinejepkemei149]

Thank you you are talented keep it up good work

[@aonodensetsu]

mod 1 is quite useful in programming, i would assume some special handling is written for it but it turns out useful

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: D this is exactly what I taught my students.

[@blackpenredpen]

: )))))

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

[@imDyne]

that was so good. thanks

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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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Smooth explanation

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Please keep uploading Number Theory videos!

[@blackpenredpen]

ok!!!!!!!!

[@alexcalabro8140]

Very good, thank you!

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Crystal clear!

[@taylahonline2038]

does anyone know what the reverse of modular arithmetic is? Im decrypting and cannot find anything on it

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THANK YOU SO MUCH!

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excellent explanation

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Great video!

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thanks this helped me pass my test

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Thank you very much

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Thank you so much

[@coin5207]

Thank you for this video

[@aparnadubey9662]

How can you solvw the equation -17 mode 7

[@nirmaljyotieducationclasse9965]

hey man how did you derive the 2 equation i am having a lot of trouble understanding that . how did you remove mod from the equvalence and all that

[@navster100]

im doing proofs with modular congruence and my head is exploding

[@GeorgeDCowley]

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

[@nuggeteater69]

Is it necessary to state that a, k, n and b are all integers? For example, would I need to write that if I was asked to give these definitions on a test?