Solving Linear Congruences, Modular Arithmetic

See how to solve Linear Congruences using modular arithmetic. See how using the TI-84 sequence command will give you the residue sequence.

[nikolajnguyen]

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.

[tombardier]

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.

[ibrahimiqbal]

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.

[personalacc]

watching this after 3 years of publishing it, you explain better than my dctrs thankssss for making it easy😍

[subramaniabharathis]

Very good explanation. Thank you, sir. Need some more examples of difficult Sums on congruence

[SequinBrain]

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.

[hs]

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)

[oliviacruz]

Thank you for explaining in detail how to solve linear congruences.

[jamesmuking]

My slides for class were horrible. This saved me from my brain fart possibly going into a brain diarrhoea into a brain dehydration

[axeldaniels]

Thanks, man. You really saved my ass on the final!

[sanjanaattanayake]

Thank you very much!
Nice teaching with clear explanations 💙

[alexl]

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.

[angeekevine]

Till now we are still appreciating your work
Really helps

[samsunnahar]

Thanks a lot for excellent explanation!!

[leviticus]

Thank you from the bottom of my heart. You are amazing. Excellent explanation!!

[firanam]

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.

[Chris-ngzi]

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.

[pinkPIGSandCUPCAKES]

Thanks so much, this made it so easy to understand

[PMe-mytd]

Thanks now we just need it for large numbers! e.g. 125452x - 4 = 4 mod 15044

[SuryaBoddu]

At 7:15 what is that parametric equation? How do we get it?