The Chinese Remainder Theorem (Solved Example 2)

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  • Опубликовано: 4 янв 2025

Комментарии • 117

  • @arastooajorian9069
    @arastooajorian9069 Год назад +67

    in the second equation (2x = 6 mod 20) when you divide both side by 2, you must divide 20 by GCD(2,20) so the result would be (x=3 mod 10)

    • @technoflash77
      @technoflash77 11 месяцев назад +7

      Yes I too felt the same ...Hope he will reply and clarify doubts of thousands @nesoacademy

    • @technoflash77
      @technoflash77 11 месяцев назад +6

      15 = 5 mod 10 if we common out 5 then it will be 3 = 1 mod 2 and not 3 = 1 mod 10.... so getting answer correct at the end of video is just a coincidence .... in short we are right 4

    • @jesusbosch2720
      @jesusbosch2720 Месяц назад

      big disappointment... this channel is usually good. they should re-make this video

    • @bambangs2036
      @bambangs2036 Месяц назад +1

      You are correct

  • @rajeshprajapati4863
    @rajeshprajapati4863 2 года назад +52

    Answer to H.W. : X = 122
    For Verification : 5 mod 3 is reducible to 2 mod 3. So, X = 122 holds for given congruent equations.

    • @preeti4534
      @preeti4534 2 года назад +3

      In Homework question, please tell me what is the value of M1^-1, M2^-1 and M3^-1?

    • @rajeshprajapati4863
      @rajeshprajapati4863 2 года назад +6

      @@preeti4534 1,2,3 respectively.

    • @harshavardhanas5799
      @harshavardhanas5799 Год назад +3

      BUT 122 IS NOT THE PRIME NUMBER

    • @pandarikathera8418
      @pandarikathera8418 Год назад

      @@preeti4534 m1 inverse=1,m2inverse=2,m3=25.

    • @nazansari9902
      @nazansari9902 Год назад +1

      HOw can we reduce the 5 mod 3 to 2 mod 3

  • @SrisailamNavuluri
    @SrisailamNavuluri 5 месяцев назад +4

    In the second set equations 4x=9q1+5,2x=20q2+6
    x=53 is the minimum value

  • @kumar-bi2ef
    @kumar-bi2ef Год назад +3

    You explained clearly sir... Keep putting new vedios.. Keep going up.. Continue rocking..
    Put more vedios.. Continue
    I will always support you sir. ..
    Very soon you will reach more & more subscribers... 🎉
    All the best...

  • @bolisettyshashank9754
    @bolisettyshashank9754 6 месяцев назад +1

    Clear explanation ❤

  • @arandomzy
    @arandomzy Год назад +5

    Answer 122, M1 = 55, M1^-1 = 1, M2 = 33, M2^-1 = 2, M3 = 15, M2^-1 =3, M = 165

  • @achugh52
    @achugh52 4 месяца назад +1

    In equation 2, we need to replace 2x = 6 mod 20 by x = 3 mod 10 for getting correct answer. (please note that 6 cannot be directly divided by 2. there will be change in mod part as well)

  • @utilizator1701
    @utilizator1701 3 года назад +12

    5:26 sorry, but x=3 mod 20 is just one of the 2 solutions. The other one is 13 mod 20.

  • @KidSite409
    @KidSite409 2 года назад +2

    Best teacher 👍

  • @SowmiyaJ-m8f
    @SowmiyaJ-m8f 4 месяца назад

    Great teach ❤

  • @partharora356
    @partharora356 Год назад +3

    @5:38 , the equation written is wrong , it should be x= 3 mod10 , we also have to divide inside the mod, eg. 10=2mod8 implies 5=1mod4 , not 5=1mod8 , so the solution is wrong

    • @GreatDG
      @GreatDG 7 месяцев назад +1

      It's incomplete, there will be 2 solutions
      3mod20 and 13mod20

  • @JarppaGuru
    @JarppaGuru 10 месяцев назад

    1:45 yes we can, but what X is? what we are calculating. where those other come? like this is private key and this cipher and x answer is private key. like real example not just this numbers. what they are?. this was exact same video but use diff numbers that other. what have to do network security?

  • @kajal5217
    @kajal5217 2 года назад +15

    2nd equation should be X=3(mod 10)
    Because cancel 2 from mod as well
    Final answer is 53

    • @amlansaikia235
      @amlansaikia235 2 года назад

      Yes I have the same doubt

    • @raghusinni
      @raghusinni Год назад

      Correct.

    • @toveyfan5097
      @toveyfan5097 Год назад

      Yea when I saw the equation just now, I immediately went to the comment section.

  • @bijeshk.s9709
    @bijeshk.s9709 Год назад +3

    5:27 i feel like we can't cancel 2 there. We can only do that if 2 and 20 are relatively prime but they are not.

    • @sanjaymandal1698
      @sanjaymandal1698 Год назад +2

      Yes wrong it will be x=3(mod10)

    • @poojasaxena41
      @poojasaxena41 4 месяца назад

      Yes , you both are correct​@@sanjaymandal1698

  • @md.nomanibnehabib3395
    @md.nomanibnehabib3395 6 месяцев назад

    The given problem states that \( X = 122 \) for mod 3, 5, and 11. We can't get \( a1, a2, a3 \) as 5, 2, and 1, respectively. Therefore, the question is incorrect. The correct values for \( a1, a2, a3 \) should be 2, 2, and 1. hope you understand , if i am wrong than let me know the correction..

  • @senugege
    @senugege Год назад

    my freind, thank you so much, you explain everything pretty simple and understandable...

  • @rohakdebnath8985
    @rohakdebnath8985 8 месяцев назад +1

    53 is the smallest positive solution. Increments by 90 will be valid as well

  • @dhairyaoza5422
    @dhairyaoza5422 2 года назад +1

    nice explaination sir

  • @monicabattacharya6416
    @monicabattacharya6416 3 года назад +2

    😃😃😃thanks sir

  • @manishaballa2720
    @manishaballa2720 2 года назад

    thank u so much sir🙏

  • @andrewgalbraith1858
    @andrewgalbraith1858 Год назад +3

    I went through the problem but fixed the error at 5:25 and got x = 53 (mod 90). Which works, but it would nice for the modulus to be 180. Here's what I did:
    x = 53 (mod 90)
    x = 90k + 53 for some integer k.
    k is either even or odd, in other words leaves a remainder of 0 or 1 when divided by 2.
    If k is even:
    x = 90k + 53 = 90(2m) + 53 = 180m + 53, where m is another integer. So, x = 53 (mod 180) is a solution.
    If k is odd:
    x = 90k + 53 = 90(2n + 1) + 53 = 180n + 90 + 53 = 180n + 143, where n is an integer. So, x = 143 (mod 180) is the second solution.

  • @jeevithar9700
    @jeevithar9700 Год назад

    Thank u sir

  • @heartofthemoon
    @heartofthemoon 5 месяцев назад

    Nice!

  • @SequinBrain
    @SequinBrain 11 месяцев назад +1

    HW: X = 122, but when 122 is divided by 3, we get 2 as the remainder, not 5 Which doesn't fit for x = 5 (mod 3). Or is X = 5 (mod 3) equivalent to X = 2 (mod 3) since 5 / 3 = r2?

    • @pathumdilharadissanayake5032
      @pathumdilharadissanayake5032 11 месяцев назад

      its correct. 5(mod 3) can be further reduced to 2(mod 3); and you can also think it as this way; 122 = 120 + 2 = 120 -3 +3 +2 = 117 +5 = 3*39 +5 which is also correct.

    • @SequinBrain
      @SequinBrain 11 месяцев назад

      @@pathumdilharadissanayake5032 thx, cuz I rechecked my math, didn't see anything wrong, saw 122 in another comment, then was confused by the 5.

  • @ultrainstinct4482
    @ultrainstinct4482 7 месяцев назад

    I think the correct ans of 2nd last (6:00) quo is 11

  • @faveuryoumbi393
    @faveuryoumbi393 Год назад +1

    Well explained

  • @mihirpopat3941
    @mihirpopat3941 3 года назад +4

    Answer of homework question:-
    X=122 mod 165

  • @KrishnaTripathi1709
    @KrishnaTripathi1709 11 месяцев назад +2

    THANKU FOR SHARING WRONG INFO 😊😊😊😊
    I LOST MY 4 MARKS BEACUSE OF YOU
    JUST REALISED U CANT JUST DIVIDE BOTH SIDES BY 2
    THANKU FOR YOUR EFFORTS

  • @jesusbosch2720
    @jesusbosch2720 Месяц назад

    at 3:24 is not clear what you are doing there...

  • @manas-tapas-Art
    @manas-tapas-Art Год назад

    Lovely❤🎉🎉🎉thank sir🎉

  • @mdnuzmolislam6450
    @mdnuzmolislam6450 Год назад

    Sir, 143*4 mod 9 also congruent to 5 mod 9. so why should i have to do 4^-1 in both sides? while i found X then we need to just multiply the X into 4 or the value that is given. Simple.

  • @salmanajaybhai
    @salmanajaybhai Месяц назад

    The multiplicative inverse of 2 mod 20 does not exist, how did you make the coefficient 2x equal to 1?

  • @Chandu-ls5jf
    @Chandu-ls5jf 3 года назад

    thanks

  • @thanmaijami8962
    @thanmaijami8962 3 года назад +6

    X=122

  • @DiyaSuri-r1h
    @DiyaSuri-r1h 10 месяцев назад

    Home question: Change 1st equation X=1(mod 3) then X will be 67 holds true for all

  • @justpaulo
    @justpaulo 3 года назад +6

    HW: X=122

    • @vamshireddy3830
      @vamshireddy3830 3 года назад

      I am getting 112

    • @justpaulo
      @justpaulo 3 года назад

      @@vamshireddy3830
      112 ≡ 2 (mod 11) since 10 x 11 = 110.

    • @utilizator1701
      @utilizator1701 3 года назад +2

      Same answer for me, but 122 mod 3 is 2, not 5.
      Edit: Nevermind. 5 mod 3 is 2.

  • @justpaulo
    @justpaulo 3 года назад +14

    Sir, I think there is an error in this video.
    X=143 indeed solves the problem, but X=53 does it also, and it is smaller.
    I think the issue is in the simplification step @ 5:26.
    You see, X = 13 solves the original equation 2X ≡ 6 (mod 20), but it's not a solution to X ≡ 3 (mod 20).
    I believe the 2nd equation simplifies to X ≡ 3 (mod 10) instead.

    • @smilealways7344
      @smilealways7344 3 года назад +1

      Yes.

    • @smilealways7344
      @smilealways7344 3 года назад

      Can I have your phone number please?

    • @rywen1
      @rywen1 3 года назад +3

      2.X=6(mod20) X=13 , a1=8,a2=13,m1=9,m2=20,M=180,M1=20,M2=9 ==> 20.M1i=1(mod9) , M1i=5 and 9.M2i=1 , M2i=9 as equation X=(8.20.5+13.9.9)mod180 , 1853 (mod180)=53 so X=53

    • @amlansaikia235
      @amlansaikia235 2 года назад

      Yes this must be correct

  • @JarppaGuru
    @JarppaGuru 10 месяцев назад

    1:10 we can read. there no need this1 this2 this thre bladiblabla

  • @CHAITHUCHANDU76
    @CHAITHUCHANDU76 10 месяцев назад +1

    X=30

  • @SuccessAccount-c4v
    @SuccessAccount-c4v Год назад

    why i am getting M I of 20 mod 9 equal to 9 using extended euclidian theorem instead of 5

  • @utilizator1701
    @utilizator1701 3 года назад +2

    Homework answer: 122.

  • @preeti4534
    @preeti4534 2 года назад +1

    Please give the explanation of homework question.

  • @heavenhitter74
    @heavenhitter74 2 года назад +1

    h/w ans is 137

  • @rohitsai4995
    @rohitsai4995 3 года назад +1

    please upload next videos also ASAP

  • @donthusravya2026
    @donthusravya2026 3 года назад +12

    I got X=122 for home work sum but in verification for first equation i.e 122 mod 3=2 but in question it is 5.How is it possible??

    • @hazemkak
      @hazemkak 3 года назад +5

      because 5(mod3)=2(mod3)

    • @aluvaja9653
      @aluvaja9653 2 года назад +2

      5%3 == 2%3

  • @baranbeytemur5451
    @baranbeytemur5451 2 года назад +1

    answer is 53

  • @_AnujJangra
    @_AnujJangra 3 года назад +7

    sir what is the meaning of neso ? it is a simple name ?

    • @mnnsi
      @mnnsi 2 года назад +2

      no it's a SO SIMPLE name

  • @adonis450
    @adonis450 Год назад

    M1 and M1 inverse gets cancelled right

  • @sagarbarman4106
    @sagarbarman4106 2 года назад +2

    Formula ka Sign Wrong hai 🙂 Congruent sign hoga, Equal sign nahi hoga

  • @Ramlal-wd2wp
    @Ramlal-wd2wp Месяц назад

    uska naam to nhi lunga lekin itna jrur kahunga ki he falani
    4X=5mod9, 2X=6mod20
    sol=143(i love you)

  • @heershah434
    @heershah434 Год назад

    2x=6mod20 -> x=3mod10 not 3mod20

  • @AditiRathore-m1d
    @AditiRathore-m1d 9 месяцев назад

    Hw. Ans. 287

  • @faveuryoumbi393
    @faveuryoumbi393 Год назад

    Im not able to find M3 inverse

  • @mamatayeul1394
    @mamatayeul1394 Год назад

    Home work answer is=122

  • @pandarikathera8418
    @pandarikathera8418 Год назад

    m3 inverse for homework is 25??

  • @Sarifyakkha
    @Sarifyakkha Год назад

    H/W Answer is x = 40 .

  • @vivekkalyan7885
    @vivekkalyan7885 9 месяцев назад

    Sir ji 😢 mere se m1×m inverse nhi nikal rha h solution btao please 😢

  • @dronamrajuchanda3262
    @dronamrajuchanda3262 4 месяца назад

    ans 53

  • @ayushjha330
    @ayushjha330 3 года назад +2

    122

  • @AmazingAtoms
    @AmazingAtoms Год назад

    for hw question im getting 98mod15

  • @saisaladi5151
    @saisaladi5151 2 года назад

    X=12

  • @kowshik_reddy_iguturi
    @kowshik_reddy_iguturi Год назад

    113

  • @stacydevries4241
    @stacydevries4241 11 месяцев назад

    Maybe 7?

  • @hendriii1991
    @hendriii1991 5 месяцев назад

    X=368

  • @ANUJTANEJA-gc1jp
    @ANUJTANEJA-gc1jp Год назад +1

    bro doesn't know how to pronounce a simple a and x, what the hell is yae yex?

  • @pavani8943
    @pavani8943 3 года назад +1

    ❤🥰🥰❤🥰🥰❤🥰🥰❤

  • @lidwinekamdoum6714
    @lidwinekamdoum6714 3 года назад +1

    X=77

  • @saadahmedkhan7017
    @saadahmedkhan7017 Год назад

    Sir apne mod toh niklana sikhaya hi nhi

  • @vamshireddy3830
    @vamshireddy3830 3 года назад +1

    112

  • @junmonirunjun1798
    @junmonirunjun1798 2 года назад

    This video is wrong

  • @bhavyachampaneri
    @bhavyachampaneri 2 года назад +2

    x=122

  • @karthikgadyal4918
    @karthikgadyal4918 Год назад +3

    HW
    X =122

  • @Chandu-ls5jf
    @Chandu-ls5jf 3 года назад +3

    X=122

  • @serfreshvlogs4119
    @serfreshvlogs4119 2 года назад +1

    x = 122

  • @arifuzzamanfahim4326
    @arifuzzamanfahim4326 5 дней назад

    X = 110

  • @ishansavaliya831
    @ishansavaliya831 Год назад

    122

  • @thotakurisaiamithchowdary849
    @thotakurisaiamithchowdary849 2 года назад +3

    X=122

  • @rich-van
    @rich-van Год назад

    122

  • @islamicqueen6423
    @islamicqueen6423 2 года назад +1

    X=122

  • @UsamaEnan
    @UsamaEnan Год назад +1

    122

  • @MamtaGupta-mo4un
    @MamtaGupta-mo4un 11 месяцев назад +1

    X=122

  • @casualgaming-su7yq
    @casualgaming-su7yq 3 месяца назад

    122