How To Find The Inverse of a Number ( mod n ) - Inverses of Modular Arithmetic - Example

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  • เผยแพร่เมื่อ 25 พ.ย. 2024

ความคิดเห็น • 248

  • @trollerxoxox
    @trollerxoxox 8 ปีที่แล้ว +77

    Thank you for explaining it so well. I hate it when some other mathematicians just show off by being cryptic, its so frustrating. Your tutorial was a tiny tad slower but made it so much easier to follow and learn. Thanks.

    • @nahiyanalamgir7056
      @nahiyanalamgir7056 2 ปีที่แล้ว +7

      The thing is that mathematicians use symbolic representations and formulas to summarize stuff in a compact way - but that's terrible for explanation. They should refrain from doing that and instead explain things in a human-friendly way!

    • @logisec
      @logisec ปีที่แล้ว +4

      @@nahiyanalamgir7056 Suffering from this right now in my Cryptography class, absolutely soul-sucking explanations in this class

  • @sharvesh0369
    @sharvesh0369 5 หลายเดือนก่อน +2

    Been searching all night for this to learn chinese remainder theorem for tomorrows network security exam. This one is a LIFESAVER

  • @c0wqu3u31at3r
    @c0wqu3u31at3r 8 ปีที่แล้ว +10

    Can I just say thank you on behalf of everyone at QMUL taking the Algorithms and Complexity module. This has really come in useful with trying to understand RSA encryption!

    • @mathhacker4764
      @mathhacker4764 10 หลายเดือนก่อน

      Same, had to learn this topic to understand RSA encryption!

    • @kingkevthebest3114
      @kingkevthebest3114 5 หลายเดือนก่อน

      man rsa encryption is 8th grade math

  • @KitKatSam27
    @KitKatSam27 6 ปีที่แล้ว +24

    This was amazing. Way better step by step explanation than my professor. THANK YOU!!

  • @amandaniess7028
    @amandaniess7028 6 ปีที่แล้ว +7

    Thank God! I have an exam tomorrow and I've never really understood how to use the algorithm to find aninverse. I like u.

  • @bensosfrequents
    @bensosfrequents 9 ปีที่แล้ว +9

    doing Bsc mathematics and computer science in pure maths section (number theory).... this tutorial has really really improved me.... i have not only understood linear congruence but also cryptology... nice and God bless you

  • @ibejoseph19
    @ibejoseph19 ปีที่แล้ว +2

    I've been looking for a video like this for weeks. After another seemingly fruitless search, I prayed and just stumbled on your well explanatory video. Thank you very much.

  • @HighFlyier11
    @HighFlyier11 8 ปีที่แล้ว +1

    RESPEK!
    Every other TH-cam tutorial should do future students of this a favor and take off their videos.
    Most clear and concise.
    Respek once again

  • @kaylaburrell4637
    @kaylaburrell4637 5 ปีที่แล้ว +5

    This makes sense now! I decrypted an affine cipher, but afterwards, I couldn’t figure out how I got -5 as the inverse of 5 or how it worked. After watching this video, I worked it out and got -5 again. Apparently, I’m just the type of person to use actual math successfully by accident.

  • @CatherineWeeks
    @CatherineWeeks 6 หลายเดือนก่อน

    Thank you so much for this! I have a discrete final coming up and it's the videos on niche topics like this that are really getting me through. You teach it so well too, thank you so much for putting your effort and time into videos like these.

  • @learnmathtutorials
    @learnmathtutorials  11 ปีที่แล้ว +2

    Thank you. Not every number in a mod field will necessarily have an inverse. For example 2 (mod 4) does not have and inverse since 2*0 = 0 (mod 4) .... 2*1 = 2 (mod 4) ... 2*2 = 0 (mod 4) ...2*3 = 2 (mod 4) ... none of these results produce 1 (mod 4) and you have checked 2*0 , 2*1 ,..., 2*(n-2) , 2*(n-1) where n is the mod.

  • @Robertlavigne1
    @Robertlavigne1 8 ปีที่แล้ว +3

    THANK-YOU!!! So intuitive when shown this way. My proff skipped a bunch of steps and it went right over my head. Much appreciated!

  • @omberry7950
    @omberry7950 2 ปีที่แล้ว

    very very thanks.. i am strugling with inverse. you solved the problem very efficiently .......

  • @Mazloum1000
    @Mazloum1000 7 ปีที่แล้ว

    better than my indian lecturer will ever explain it with her annoying accent, thank you good sir, and this definitely warrants a subscribe

  • @arefinahammed8408
    @arefinahammed8408 7 หลายเดือนก่อน

    after 10 years. Thank you. Was going crazy :')

  • @AndrewBaba
    @AndrewBaba 9 ปีที่แล้ว +10

    The best explanation on the youtube I found so far. Thank you

  • @josephcario2659
    @josephcario2659 8 ปีที่แล้ว

    boss tnx now I can explain it very well to my students.there are lots of video related to this bt this clearly explains the topic.nice...

  • @iamriotus
    @iamriotus 9 ปีที่แล้ว +9

    Absolutely amazing tutorial! Preparing for my exam, I couldn't find a good explanation anywhere! You really saved my bacon!

  • @shaheershakeel6851
    @shaheershakeel6851 2 ปีที่แล้ว

    Thank you! This was the best explanation of EA and EEA I've been through. I still have no idea why tf this thing exists though

  • @RobinsonGames
    @RobinsonGames 5 ปีที่แล้ว +8

    This really helped a lot. Feeling much more prepared for my exam now

  • @sethmarcus1784
    @sethmarcus1784 5 ปีที่แล้ว

    Excellent video clearly demonstrating how to calculate the inverse of a number(mod n). Very grateful for this video!

  • @mahendrakotapati9970
    @mahendrakotapati9970 5 ปีที่แล้ว +1

    you had explained in very clear manner thanks sir...

  • @hafilahmustaffa
    @hafilahmustaffa 3 ปีที่แล้ว

    thank you so much. I spend a day to find the solution for d equal to negative. Superb.

  • @learnmathtutorials
    @learnmathtutorials  11 ปีที่แล้ว +11

    If that is the case, I would guess that you simplified a little early. When doing this process, it is important to leave terms as multiples of two numbers, so that one of the numbers can be replaced by an equation above. I hope that helps. :)

  • @HypnotizeCampPosse
    @HypnotizeCampPosse 10 ปีที่แล้ว

    Learn Math Tutorials I like how you solved for the remainder values first in the video, then went and did the Reverse Eulcidean Algo (REA) This method is different from every other method I have seen demonstrated (where they do the REA and computer the replacement values on-the-fly). I think you way will keep me organized better, thanks for making the video.

  • @NandaAcademies
    @NandaAcademies 3 ปีที่แล้ว

    Excellent explanation which is useful in understanding RSA algorithm.

  • @evermoregwatiwa8001
    @evermoregwatiwa8001 5 ปีที่แล้ว

    this is the best explanation ever. thumps up man.

  • @PhamQuang
    @PhamQuang 4 ปีที่แล้ว

    Having an exam coming next week. You saved me. HUGE THANKS

  • @p1q2r
    @p1q2r 4 ปีที่แล้ว

    The best explanation for modular multiplicative inverse.. Thanks much!

  • @TaylorCaRRtel
    @TaylorCaRRtel 9 ปีที่แล้ว +3

    Studying for my final and couldn't figure this out for the life of me. Your explanation was great. Thank you

  • @anmaraljanabi7137
    @anmaraljanabi7137 8 ปีที่แล้ว +8

    Thanks you very much sir, wish you continues success

  • @amarachiukor4016
    @amarachiukor4016 3 ปีที่แล้ว

    Your explanations on this topic is so on point. Thanks alot

  • @MAGonzzManifesto
    @MAGonzzManifesto 10 ปีที่แล้ว +4

    Thank you so much! I feel confident doing these kinds of problems now!

  • @blacklotus5953
    @blacklotus5953 5 ปีที่แล้ว

    Great explanation! Way better than my lecture at uni

  • @CylenxswizinSim
    @CylenxswizinSim 3 ปีที่แล้ว

    Thanks so much THIS IS EXACTLY WHAT WAS MISSING IN OTHER VIDEOS MUCH APPRECIATION!!!!

  • @MultiDman2011
    @MultiDman2011 2 ปีที่แล้ว +1

    Thank you so much for making this understandable and easy to follow. Life saver!!

  • @danielbuckley9651
    @danielbuckley9651 7 ปีที่แล้ว +3

    Very nice video, good use of colours. Excellent explanation of the Euclidean algorithm leaving no steps out. Well done.

  • @adangonzales8085
    @adangonzales8085 10 ปีที่แล้ว +8

    5 Star rating for this video!

  • @ethansimmons82
    @ethansimmons82 4 ปีที่แล้ว

    I should've found this video first! It was very clear, thank you.

  • @declanallan885
    @declanallan885 7 ปีที่แล้ว +2

    awesome video dude, love how you used the different colour schemes to segregrate some of the concepts behind what was going on!

  • @JPfromDport
    @JPfromDport 8 ปีที่แล้ว

    Great video, helped me understand how to deal with negative numbers in Bezout's theorem.

  • @mathhacker4764
    @mathhacker4764 10 หลายเดือนก่อน +1

    Thanks sooooo much.

  • @sillupiiks
    @sillupiiks 6 ปีที่แล้ว

    Thank You so much! I spent an hour with my teacher today and I think now I finally got the idea:)

  • @nadianoormohamed4432
    @nadianoormohamed4432 7 ปีที่แล้ว +1

    great video!!!!! You explain it in a structured way which is essential for a topic as such. Thanks!

  • @greatgymdj
    @greatgymdj 10 ปีที่แล้ว

    Very nice video, my lecturer just expected us to guess how to do this! Thanks :)

  • @CptGankbawlz
    @CptGankbawlz 11 ปีที่แล้ว +1

    Thank you so much! While reading my book I was completely lost! You made this so simple to follow and understand. Thanks again!

  • @gabrielsotolongo8407
    @gabrielsotolongo8407 8 ปีที่แล้ว +3

    Great tutorial! All this can be avoided by using matrix multiplication which is a faster and easier route to get the multiplicative inverse of 27 mod 392. It is always good to know both ways of course, but like I said, great tutorial! Maybe I should do a tutorial on how to do it using matrices...

    • @jackbinding5587
      @jackbinding5587 8 ปีที่แล้ว

      +Gabriel Sotolongo Im curious to how you do it with matrices! haha

    • @gabrielsotolongo8407
      @gabrielsotolongo8407 8 ปีที่แล้ว

      +Jack Binding it is really easy, I could make a video an upload it if you like, anyways there is none here in TH-cam of that type.

    • @jackbinding5587
      @jackbinding5587 8 ปีที่แล้ว

      +Gabriel Sotolongo if you do decide to make one defo tell me! Haha

    • @gabrielsotolongo8407
      @gabrielsotolongo8407 8 ปีที่แล้ว

      +Jack Binding I will try to make the video today (no promises) ;)

    • @jackbinding5587
      @jackbinding5587 8 ปีที่แล้ว

      haha, im grateful if you upload it any time man! I've just not seen anything modulo been solved with matrices so im just curious!

  • @김찬호-f1e
    @김찬호-f1e 3 ปีที่แล้ว

    Thanks you!! it is really helpful for me to understand.

  • @vestigialSmile
    @vestigialSmile 5 ปีที่แล้ว

    Thanks man! Came in handy with Abstract Algebra

  • @danielmartino8068
    @danielmartino8068 4 ปีที่แล้ว

    Thank you for the explanation, you say me a lot of theory

  • @bharathraj1646
    @bharathraj1646 4 ปีที่แล้ว +2

    Thanks a lot , it was very helpful. Could you please make more videos on modular arithmetic
    algorithms . It would really help me a lot. Thanks once again :)

  • @ajk7151
    @ajk7151 5 ปีที่แล้ว

    awesome explanation! looking forward to check out the rest of the videos. :)

  • @TheGamerViewer
    @TheGamerViewer 6 ปีที่แล้ว

    Thank you so much! best guy on youtube for this tutorial!

  • @learnmathtutorials
    @learnmathtutorials  11 ปีที่แล้ว +1

    1001 = 200(5) + 1 Rewrite as 1 = 1001 + 200(-5) (mod 1001) Note that 1001 (mod 1001) = 0 and also (-5) (mod 1001) = 996 since 1001 - 5 = 996 then we have 1 = 0 + 200(996) therefore 1 = 200(996) (mod 1001) Then 996 is the inverse of 200 (mod 1001) You can check the result by looking at 996(200) = 199200 = 199(1001) + 1 (mod 1001) and anything times the mod is 0 so we get 996(200) = 1 (mod 1001) I tried to format this nicely but it gets all jumbled together when I post it as a comment.

  • @CSBIBLE21
    @CSBIBLE21 4 ปีที่แล้ว

    this was very good, exactly what i was looking for

  • @shanthakumar1833
    @shanthakumar1833 5 ปีที่แล้ว

    Thanks a lot. Searching the answer for asymmetric key cryptography

  • @adzplus1
    @adzplus1 3 ปีที่แล้ว

    It did help to explain what the textbook had in written words and figures...but it is still difficult because you still have to go through all the numbers on the Euclidean algorithm to get to the bottom of this. So imagine if you have a gcd(80, 98) it would be endless!!

  • @Arkansas28
    @Arkansas28 3 ปีที่แล้ว

    Excellent, thanks for the video.

  • @savantdude
    @savantdude 5 ปีที่แล้ว

    amazing explanation! saved me a lot of time!

  • @kingsleyobi7482
    @kingsleyobi7482 5 ปีที่แล้ว

    Wonderful tutorial!!

  • @amazingmanish
    @amazingmanish 7 ปีที่แล้ว

    Clear cut explanation.

  • @yifuxero9745
    @yifuxero9745 11 หลายเดือนก่อน

    Much easier way:. With a pocket calculator perform the Euclidean algorithm procedure to get the continued fraction quotients and the convergent, = [14, 1, 1, 13] and underneath we have the convergents [ 1/14, 1/15, 2/29 and 27/392} With an even number of terms in the partial quotient part (we have four), we take the 392 (rightmost denominator) and subtract the denominator to the left (a 29), giving 363, (correct.). However, if the number of quotients is odd, just extract the denominator to the left of the rightmost. Example: Fine 2^(-1) mod 29. Our data is [14, 1, 1]. and underneath we write[ (1/14, 1/15, 2/29]. Denominator to left of the 29 = 15 (correct, since 2 * 15 = 1 mod 29.

  • @richardwalters9249
    @richardwalters9249 6 ปีที่แล้ว +3

    This is a great instructional video ... I still need to clean up some details in my understanding ... but this question: Is there a check you can do to verify the answer ? I’m trying to do 27^-1 (mod 292) compared to 363 ( mod 392) ... or, am I thinking about this wrong ?

  • @aadilmufti4933
    @aadilmufti4933 6 ปีที่แล้ว

    Great explanation!

  • @Tuzkichen
    @Tuzkichen 7 ปีที่แล้ว

    very clear explanation, thanks!

  • @bernie8571
    @bernie8571 10 ปีที่แล้ว +2

    wow thank you for making this. it helped a ton!

  • @Ringcaat
    @Ringcaat 2 ปีที่แล้ว

    Nice video! I just wish you hadn't chosen an example where the quotient and remainder of the first division are both 14s. And then we have two 1's later on as well.

  • @AndrewT34pot
    @AndrewT34pot ปีที่แล้ว

    thank you, well explained video

  • @atomic_godz
    @atomic_godz 10 ปีที่แล้ว

    Just what I needed, thanks a lot man

  • @rinzinnorbu3518
    @rinzinnorbu3518 5 ปีที่แล้ว

    very good expatiation thank you

  • @hilufabebe4721
    @hilufabebe4721 2 ปีที่แล้ว

    best explanation

  • @darrenmau1942
    @darrenmau1942 9 ปีที่แล้ว

    Well explain, good example, thank you very much that helps so much

  • @santiagowhite5467
    @santiagowhite5467 4 ปีที่แล้ว

    So easy to understand ty

  • @coldair0010
    @coldair0010 11 ปีที่แล้ว +3

    what if i am left with a constant on the left at the end

  • @chnoco
    @chnoco 6 ปีที่แล้ว

    Thank you so much this is so useful great job!

  • @ZeeshanAhmad-xt4pi
    @ZeeshanAhmad-xt4pi 6 ปีที่แล้ว

    so nice explanation .

  • @shivanineharkar2571
    @shivanineharkar2571 2 ปีที่แล้ว

    Dude you have helped alot😇😇😇😇😇😇😇

  • @totasalam7060
    @totasalam7060 9 ปีที่แล้ว

    thank you sooo much .. u r the best

  • @christanjhayyap2015
    @christanjhayyap2015 4 ปีที่แล้ว

    This is very helpful

  • @akamfoad
    @akamfoad 4 ปีที่แล้ว

    great thanks for the explanation!

  • @SomeOne-el9mr
    @SomeOne-el9mr 6 ปีที่แล้ว

    Thanks. You helped me alot

  • @JohnSmith-kf1lq
    @JohnSmith-kf1lq 10 ปีที่แล้ว +1

    Very helpful. Thanks for making

  • @billyandej
    @billyandej 3 ปีที่แล้ว

    I hope you’ll answer this question right away. Badly needed. We’re going to report this topic this coming Thursday.
    May I know why do we need to get the multiplicative inverse of the given? just like in the example. Why do we need to get the inverse of 27 (mod 392) and it should be congruent to 1 mod 392?

  • @rasberybanana
    @rasberybanana 9 ปีที่แล้ว +1

    very helpful video, are the equal signs at the end supposed to be congruence signs?

  • @gaoelnlaojehc8913
    @gaoelnlaojehc8913 3 ปีที่แล้ว

    why underrated?

  • @readogamer3515
    @readogamer3515 6 ปีที่แล้ว

    great! great!! great!!! explanation

  • @abhijithbalan5107
    @abhijithbalan5107 3 ปีที่แล้ว

    Thanks a Lot Sir

  • @shushmitam.s7884
    @shushmitam.s7884 6 ปีที่แล้ว

    Great tutorial! :)

  • @vash47
    @vash47 10 ปีที่แล้ว

    Thank you so much, mate.

  • @legendsplayground7017
    @legendsplayground7017 6 หลายเดือนก่อน

    I was struggling with inverse modulo, I tot decimal can have remainder what.... Thanks, love your content, Jesus bless 💪

  • @SaramZafar
    @SaramZafar 3 ปีที่แล้ว +4

    When you didn't explain why you replaced -29 with 363 I lost you, I mean it's unique to this question only. in other problems how will we know what to replace or we should even replace or not? You must have explained it a bit.

    • @ShivamSharmabtp
      @ShivamSharmabtp 3 ปีที่แล้ว

      29+363 = 392. u can check out his -ve number modulo video

  • @sjskong
    @sjskong 5 ปีที่แล้ว +1

    Thanks!

  • @SiilverEdit
    @SiilverEdit ปีที่แล้ว

    for those whom are confused
    second step after euclidean algorithm
    is
    linear combination

  • @medadrufus
    @medadrufus 9 ปีที่แล้ว

    Thanks this is awesome!

  • @apondikevinomondi5003
    @apondikevinomondi5003 7 ปีที่แล้ว +1

    You rock. Thanks a lot

  • @fkrtna
    @fkrtna 6 ปีที่แล้ว

    Wish if I watched this b4 the exam!

  • @u10100160
    @u10100160 ปีที่แล้ว

    謝謝你!!!

  • @umeshstudypoint7495
    @umeshstudypoint7495 4 ปีที่แล้ว

    Very helpful

  • @Swoost
    @Swoost 4 ปีที่แล้ว +2

    should include an explanation for this part: 9:00 my teacher would need a proof that these are equivalent modulo

  • @philteng760
    @philteng760 3 ปีที่แล้ว

    Thank you.