Number Theory | Linear Congruence Example 2

We solve a linear congruence, while reviewing the appropriate results that make our solution valid.

[poppycock]

Almost every video I've seen so far has had a different explanation... so far I think this one makes the most sense for me, thank you!

[meaty]

I understand how the inverse part can be a bit tricky for people to understand, since he did not explain it very clearly, so I'll show you how you can think instead. When you come to the part of 5x congruent to 2 for mod 9, imagine the list of numbers that 2 could be instead of 9. By adding 9 to 2 repeatedly, you'll get said list. The list you get is 2, 11, 20, 29, 38.... Here you see that 20 is divisible by 5, such that we can get that 5x/5 is congruent to 20/5 for mod 9, which is equal to x congruent to 4 for mod 9, and there you have your answer.

[richard-]

I’m a retired life long learner who has always been interested in maths and number theory/math Olympiad problems is my current buzz. These videos are really great for bringing out the big points that might get missed with self study.

[ocnhim]

bro looks jacked.. i think bro's worth listening to

[noahrubin]

For sure the best explanation out there!

[maxzriver]

140x = 56(°252 )
simplificando
5x = 2(°9 )
5x = 20(°9 )
x = 4(°9 )

[georgesadler]

Professor Penn, Thank you for a brilliant example on Linear Congruence.

[jarrydbrennan]

BRILLIANT! Thank you for helping me see it

[crossugo]

The inverse part was a bit rushed, but this video is one of the best on congruences so far. Thanks a lot!

[farihasifat]

Much much-needed information is covered. Thank you so much.

[vaggelismanousakis]

what do we do when the number 56 is raised in a very high power ? For example I was given this one: 8x ≡ 11^41 (mod 51) but I can't figure out how to solve it.

[PunmasterSTP]

I think this video was...modul-awesome! Thanks again for sharing.

[gegiojonjongegio]

I don't really get why there are only 28 solutions, I mean, if you say x=4+9*53 for example it still works

[juanroldan]

There won't be more modular arithmetic videos?

[Meenimie]

Why didn't he give the link to the previous video he mentioned?

[gautamwarvatkar]

Ttooo good both the maths and the back ❤❤

[canyoupoop]

4:43 you can write 4k+9 where k belongs to *N* and -1 <k < 28

[bolleholle]

Why are there not infinite solutions of the form x=4+9n?

[holyshit]

Two ways of finding inverse
1. Eulers theorem
2. Extended Euclid's algorithm
Extended Euclid's algorithm is more efficient

[pramod]

TF zuckerberg explained us this easily