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.
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.
You are very good at explaining in a calm and simple way, while maintaining a very good pace. It makes it easy to follow the steps and understand where the different numbers are coming from, when you do the calculations. Thank you for the video. Sincerly a student from Denmark.
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.
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)
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.
@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!
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.
@@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.
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?
2:35 Yeah the tip is good and all but it bugs me that you should specify that the other number should NOT be a multiple of the prime This case says that GCD(7,28)=1 cuz 7 is prime which is wacky👍
@@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.
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..
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.
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.
You are very good at explaining in a calm and simple way, while maintaining a very good pace. It makes it easy to follow the steps and understand where the different numbers are coming from, when you do the calculations. Thank you for the video. Sincerly a student from Denmark.
Very good explanation. Thank you, sir. Need some more examples of difficult Sums on congruence
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.
watching this after 3 years of publishing it, you explain better than my dctrs thankssss for making it easy😍
Thank you very much!
Nice teaching with clear explanations 💙
Amazing -- clear and concise.
Thanks so much, this made it so easy to understand
Thank you for these videos.
Really helps, finally understand it!
Really helpful. Thank you very much.
great work sir. Appreciated.
You are amazing!!! Thank you for this!
Gave full clarity about solutions
Thank you sir.
Great work....!
Thanks, extremely good
Great explanation thank you❤
Thank you so much!
Thank you from the bottom of my heart. You are amazing. Excellent explanation!!
Comments like this keep me going. I really appreciate your kind words. Cheers, -Andy
Thank you!
amazing explanation tysm
WOW, I loved th eplaning of the video.
Thank you so much
thanks for this
best explanation of congruences
great work!!!!!!!!!!!!!
thank you ❤
Thank you for explaining in detail how to solve linear congruences.
You’re very welcome. These are weird, don’t you think?
My slides for class were horrible. This saved me from my brain fart possibly going into a brain diarrhoea into a brain dehydration
thanks
Thanks a lot for excellent explanation!!
You’re welcome. Have a good one!
Thanks, man. You really saved my ass on the final!
You're welcome. Seems like this particular video does a lot of that. 🙂
Real good
THANKS!!!!!
Till now we are still appreciating your work
Really helps
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.
Thanks I love you
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)
Good question. Perhaps post this question on r/mathquestions on reddit.
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.
At 7:15 what is that parametric equation? How do we get it?
lifesaver..
Amazing 🤌🏼✨
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?
greattttttttttt👌
Thanks a lottttttttt 💓
Glad this video helped you!
at 2:09, for no solution, is there a reason 2 must divide 51? Where does this conclusion derive from?
@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!
Same question. How did you come up with (mod 6) instead of (mod 2)
@@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).
Probably a editing mistake
THE ABSOULE BEST
can you explain the parametric equation a bit further?
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.
Yes, they do end up the same value. The idea is to finish with the smallest number.
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.
Hi. This was as easy an explanation as I could do.
@@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.
I love you
Thanks now we just need it for large numbers! e.g. 125452x - 4 = 4 mod 15044
Oh my, that's a good problem for...someone else.
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?
Actually I'm not sure.
5:44 At this part, can you do it without dividing the modulo?
No, somehow you need 9x to become just x.
why I feel like having Ross in my head? LOL
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?
2:35 Yeah the tip is good and all but it bugs me that you should specify that the other number should NOT be a multiple of the prime
This case says that GCD(7,28)=1 cuz 7 is prime which is wacky👍
Good point.
wow, if I do not know the mod? and only know a and b? what I have to do?
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.
@@aborne there is not offense.. I just want to learn..thats all
@@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.
@@aborne thank you!
if you write an audio book on math you will definitely help infinity pips, and you will get some serious money
Thank you for those kind words. What’s are infinity pips?
@@aborne ok, i meant you could help infinity people 👌👍
BAYES theorem.
no
Dear :
could you check your e-mail
Thank you so much
may I get ur email
Go to www.andyborne.com/math and you will find it there.
Can you help me with this, please:
x ≡ 2 (mod 11)
x ≡ 9 (mod 15)
x ≡ 7 (mod 9)
x ≡ 5 (mod 7) ?
Those are some good ones. I advise you approach your instructor, Teaching Assistant, or professor on help with those.
Chinese remainder theorem?
@@sujaynaik1320
There is a problem in the second row.
I took the exams. I hoop soon I will have a time and I'll write the solution.
@@ivayloivanov5766 okay!!
"One of the numbers is prime? The GCD is 1."
Not true.
GCD(prime, n*prime)=prime1
That’s a good point.
Nice from pakistant
I STILL DONT IT
IM SO DUMB
Don’t worry. Lots of people don’t getting this and they end up fine in life.
@@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 :(
I am a primate
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..
Don’t give up on yourself. Start small and slowly work in more difficult examples.
Thank you!