Applications of primitive roots -- Number Theory 19

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20:12 for when he points to a 3 which is supposed to be an 8, and says "six"

mrphlip

This is basically the last thing as the previous video on the playlist? It's almost exactly the same content, just presented in a very very very slightly different way.

QuantumHistorian

23:38 Homework
23:57 Good Place To Stop

goodplacetostop

Have u ever wanted to see Michael tipsy? Let's get Michael to do a 'Applications of Primitive Roots - The Cocktails Version' where he sips on Pina Coladas while telling us all about primitive roots!

lolanifenring

On the board it says "Video 18", and the problems and theorems seem to be the same as the last video. It feels like the wrong video is uploaded?

Bodyknock

Spoiler alert:

For those who want to check the warm-ups.

Solve 3x^14 ≡ 2 mod 23.
Notice the following:
8*3 = 24 ≡ 1 mod 23, so 8 is the multiplicative inverse of 3 (mod 23). We can solve x^14 ≡ 8*2 ≡ 16 mod 23.
Note that 3 is not a primitive root of 23, but 5 is.
5^8 ≡ 16 mod 23.
Solutions are x ≡ 9 or 14 mod 23.

Solve 13^x ≡ 5 mod 23.
Notice the following:
13 is not a primitive root of 23. In fact ord_23(13) = 11, so {13^k | 1<=k<=11} can only generate 11 of the 22 integers which are relatively prime to 23 and less than 23. It turns out that 5 is not one of them and there won't be any solutions to the problem.
To attempt a solution, note that 13 ≡ 5^14 mod 23. You should find that 14x ≡ 1 mod 22 has no solutions (from lack of even-odd parity).

RexxSchneider

This is really weird, this is like a second, different, recording of the previous video. He’s wearing a different shirt and everything…?

noahtaul

Exercise: what if it's mod 17^2 or 19^2 or some other power of those primes?

jplikesmaths

Excelente solucion, lástima que no hablo inglés🤣💔

TUTORIAS-BETANCO

Are you straight, or straight?! 😀😉 ...

klementhajrullaj

Applications of primitive roots -- Number Theory 19

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Applications of primitive roots -- Number Theory 19

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