2:30 Correction: the gcd of a prime and another integer isn't always 1. For example if the gcd of a prime and its multiple, like gcd(7, 14) = 7.
@tombardier3 жыл бұрын
Great explanation. I've been banging my head against the desk trying to get some of this stuff in to my head. This helped a lot, and approached it from quite a different perspective than my study material.
@srijanadh2303Ай бұрын
Fr Why can i imagine you banging your head ?lmao I can really imagine it 😂
@ibrahimiqbal8388 Жыл бұрын
The way you explained this topic needs to be appreciated. I was going through a difficult time to understand this but Thank You for making this topic easy for me.
@personalacc42197 ай бұрын
watching this after 3 years of publishing it, you explain better than my dctrs thankssss for making it easy😍
@jamesmuking2 жыл бұрын
My slides for class were horrible. This saved me from my brain fart possibly going into a brain diarrhoea into a brain dehydration
@SequinBrain Жыл бұрын
Excellent work detailing the specific steps in the process and not skipping any. TI-89 also has seq( from pushing 2nd > Math > List. Parameters seem to be the same.
@angeekevine9 ай бұрын
Till now we are still appreciating your work Really helps
@oliviacruz3839 Жыл бұрын
Thank you for explaining in detail how to solve linear congruences.
@aborne Жыл бұрын
You’re very welcome. These are weird, don’t you think?
@subramaniabharathis3 жыл бұрын
Very good explanation. Thank you, sir. Need some more examples of difficult Sums on congruence
@hs11132 жыл бұрын
Suppose that a and b are integers such that a ≡ 34 (mod 83) and b ≡ 21 (mod 83). Find an integer c such that 0 ≤ c < 83 such that 47c ≡ (53a−2 + b5)(mod 83)
@aborne2 жыл бұрын
Good question. Perhaps post this question on r/mathquestions on reddit.
@bugganaumadevi9413 жыл бұрын
Gave full clarity about solutions
@berat55322 жыл бұрын
best explanation of congruences
@axeldaniels96773 жыл бұрын
Thanks, man. You really saved my ass on the final!
@aborne3 жыл бұрын
You're welcome. Seems like this particular video does a lot of that. 🙂
@sanjanaattanayake4231 Жыл бұрын
Thank you very much! Nice teaching with clear explanations 💙
@calebpresto868422 күн бұрын
You can't just divide both sides of a congruence by any integer (even though you can multiply by any integer. You have to first see if gcd(n, m)=1. Only then can you divide by n.
@samsunnahar91752 жыл бұрын
Thanks a lot for excellent explanation!!
@aborne2 жыл бұрын
You’re welcome. Have a good one!
@Ligaya_Reyes2 ай бұрын
Thank you so much! i understand it a lot
@leviticus34 жыл бұрын
Thank you from the bottom of my heart. You are amazing. Excellent explanation!!
@aborne4 жыл бұрын
Comments like this keep me going. I really appreciate your kind words. Cheers, -Andy
@sebastianm5047 Жыл бұрын
Amazing -- clear and concise.
@Damsengeedana5 ай бұрын
Great explanation thank you❤
@PMe-my1td2 жыл бұрын
Thanks now we just need it for large numbers! e.g. 125452x - 4 = 4 mod 15044
@aborne2 жыл бұрын
Oh my, that's a good problem for...someone else.
@bruh-nk5wb6 ай бұрын
amazing explanation tysm
@ayushkumar23102 жыл бұрын
great work!!!!!!!!!!!!!
@nenani18173 жыл бұрын
WOW, I loved th eplaning of the video.
@pinkPIGSandCUPCAKES4 жыл бұрын
Thanks so much, this made it so easy to understand
@ambilyfrancis58792 жыл бұрын
Really helpful. Thank you very much.
@senadkhalfa83743 жыл бұрын
thanks
@prudhvik56032 жыл бұрын
great work sir. Appreciated.
@firanam73163 ай бұрын
Is there any good manual method to find the needed number at 4:06? Due to the nature of my course I am unable to use electronic supplements such as calculators, and while the method "works", it's painfully slow for larger numbers, for instance I have the congruence 61x≡205 (mod 788) - with digital methods I found that the number I'd need would be -20*788+205 = -15555 - easy to obtain digitally but rather time-consuming manually.
@paulmacdonald51953 жыл бұрын
Thank you for these videos.
@saradekeijzer84573 жыл бұрын
Really helps, finally understand it!
@jblkpnthr3 жыл бұрын
You are amazing!!! Thank you for this!
@nimnanilwala52454 жыл бұрын
Thank you sir. Great work....!
@SuryaBoddu2 жыл бұрын
At 7:15 what is that parametric equation? How do we get it?
@beatrizrosa61893 жыл бұрын
Thank you so much!
@YT.ASMR.DRW. Жыл бұрын
thank you ❤
@mora81814 жыл бұрын
Thanks, extremely good
@user-fr5be6gy3u3 жыл бұрын
Thank you!
@mixinfo62023 жыл бұрын
Thank you so much
@tazkiakamalia3 жыл бұрын
thanks for this
@Chris-ng9zi2 жыл бұрын
I got lost at the stage where you introduced the parametric equation. I know that a "congruent to b (mod n") means a= n.k +b. So b=a - n.k and so I am confused about b= 2t + 0.
@AyushPatel Жыл бұрын
THANKS!!!!!
@luxjoseph25963 жыл бұрын
why I feel like having Ross in my head? LOL
@haru_ne_2 жыл бұрын
Thanks I love you
@a.c.46193 жыл бұрын
So how do you take it a step further by getting the actual solution(s) for "x" using the Euclidean Algorithm? Some sites use the variables "s" and "t". I'm just looking for an easier explanation.
@aborne3 жыл бұрын
Hi. This was as easy an explanation as I could do.
@a.c.46193 жыл бұрын
@@aborne I apologize for not making myself clear. I didn’t mean that I wanted an explanation simpler than the one you provided. Your explanation was excellent and easy to understand. It’s just that my textbook asks for us to delve further. Your explanation stops at simply trading one congruence modulo for another. In other words, your explanation is simply taking a congruence modulo in the form of [ax ≡ b(mod m)] into another congruence modulo of the same form only with different variables [cx ≡ d(mod m)] Again, your explanation was great. My textbook, however, does not want answers in the form of another congruence modulo. It asks for “solutions” to the original congruence modulo by utilizing the Euclidian Algorithm. The book wants it written as an equality rather than a congruence. For example, my book has the following problem: 20x ≡ 14(mod 63) I’m fairly certain that I could use your explanation to derive another congruence modulo (like you did) as follows: x ≡ 7 (mod 63) However, the textbook shows the answer written as an equality as follows: “x = -308 is a solution.” When I stated that I was searching for an easier explanation, I meant an easier explanation than my textbook and an easier explanation than other sites I’ve searched. Sorry for the ambiguity.
@emmaruhcheva3658 Жыл бұрын
lifesaver..
@nigelkay62643 жыл бұрын
if you write an audio book on math you will definitely help infinity pips, and you will get some serious money
@aborne3 жыл бұрын
Thank you for those kind words. What’s are infinity pips?
@nigelkay62643 жыл бұрын
@@aborne ok, i meant you could help infinity people 👌👍
@cinderbane1 Жыл бұрын
Is the rule about GCD between at least one prime number always true? What about GCD(24,3) as an example? Isn't that = 3?
@The.mohisa6 ай бұрын
Amazing 🤌🏼✨
@chandler2003 жыл бұрын
greattttttttttt👌 Thanks a lottttttttt 💓
@aborne3 жыл бұрын
Glad this video helped you!
@robertoberidojr.4354 жыл бұрын
Real good
@what-it-izz3 жыл бұрын
at 2:09, for no solution, is there a reason 2 must divide 51? Where does this conclusion derive from?
@farouqalsalih6192 жыл бұрын
Isn’t there a rule you have to follow when multiplying or dividing a number to the congruence, like it has to be coprime to the modulo number?
@aborne2 жыл бұрын
Actually I'm not sure.
@michaeljacobdelossantos Жыл бұрын
5:44 At this part, can you do it without dividing the modulo?
@aborne Жыл бұрын
No, somehow you need 9x to become just x.
@lmatton13 жыл бұрын
can you explain the parametric equation a bit further?
@kairiannah3 жыл бұрын
THE ABSOULE BEST
@davidkam36610 ай бұрын
At 1:06 , i dont think{...-27,-19,-11,-3,5,13,21,29,36...} it is the least residues system modulo 8, because they have the same remainder 5. Are u telling wrong?
@imranif38993 жыл бұрын
@Andrew Borne Awesome as always. Just a tiny question for 7:15 , how did you come up with x congruent to b (mod 6)? why isn't it (mod 2) Thanks in advance!
@janslittleclassroom6659 Жыл бұрын
Same question. How did you come up with (mod 6) instead of (mod 2)
@charlenegwin2162 Жыл бұрын
@@janslittleclassroom6659 I don't know why, but at 7:29 he says that the solutions have to be in terms of the original mod => 9x≡ 42 (mod 6).
@hvcreator2380 Жыл бұрын
Probably a editing mistake
@miraculix6663 жыл бұрын
"One of the numbers is prime? The GCD is 1." Not true. GCD(prime, n*prime)=prime1
@aborne3 жыл бұрын
That’s a good point.
@MrKrabs-xf2tr3 жыл бұрын
On the first problem of the one solution set, why must you look down to 6 and not 20? Is there a reason or do they all end up as the same value.
@aborne3 жыл бұрын
Yes, they do end up the same value. The idea is to finish with the smallest number.
@quetzaltpa44503 жыл бұрын
wow, if I do not know the mod? and only know a and b? what I have to do?
@aborne3 жыл бұрын
I mean no offense; if you are asking these questions you are studying mathematics that is a little too advanced for you at this time.
@quetzaltpa44503 жыл бұрын
@@aborne there is not offense.. I just want to learn..thats all
@aborne3 жыл бұрын
@@quetzaltpa4450 Mod is short for modulo. It is sometimes represented by the this symbol, %. It is the remainder of division, for example #1, 5 mod 2 means 5 ÷ 2 = 2 with a remainder of 1. So the answer of 5 % 2 = 1. Example #2, 23 mod 5 means 23 ÷ 5, which is 4, and the remainder is 3. That means, 23 mod 5 = 3. To answer these questions in the video, you will need all three numbers a,b and c. If you are not provided with the number c, then you will need to ask the person who assigned the exercise question.
@quetzaltpa44503 жыл бұрын
@@aborne thank you!
@ivayloivanov5766 Жыл бұрын
Can you help me with this, please: x ≡ 2 (mod 11) x ≡ 9 (mod 15) x ≡ 7 (mod 9) x ≡ 5 (mod 7) ?
@aborne Жыл бұрын
Those are some good ones. I advise you approach your instructor, Teaching Assistant, or professor on help with those.
@sujaynaik132011 ай бұрын
Chinese remainder theorem?
@ivayloivanov576611 ай бұрын
@@sujaynaik1320 There is a problem in the second row.
@ivayloivanov576611 ай бұрын
I took the exams. I hoop soon I will have a time and I'll write the solution.
@sujaynaik132011 ай бұрын
@@ivayloivanov5766 okay!!
@ciromaiello41113 жыл бұрын
I love you
@vishaldonda2 жыл бұрын
BAYES theorem.
@nasserkhamis16902 жыл бұрын
Dear : could you check your e-mail
@tsunningwah34718 ай бұрын
no
@nasserkhamis16902 жыл бұрын
Thank you so much may I get ur email
@aborne2 жыл бұрын
Go to www.andyborne.com/math and you will find it there.
@Ahnos11 ай бұрын
I STILL DONT IT IM SO DUMB
@aborne11 ай бұрын
Don’t worry. Lots of people don’t getting this and they end up fine in life.
@Ahnos11 ай бұрын
@@aborne I have exam today that's why I'm trying to push this thing to my brain but it just doesn't go in :(
@piotrek76337 ай бұрын
I dont understand any of this, books are too complicated if your basics arent correct and there isnt any material in simple terms. Kinda doomed im hoping to memorise everything and get it over with..
@aborne7 ай бұрын
Don’t give up on yourself. Start small and slowly work in more difficult examples.