lmao, what if a want to mult by 3 mod 9

0:48 are those Stardew Valley sound effects 🤔

Julia set

Nice

What happens if you take the limit at infinity on prime factors? What does mod infinity look like if we can say it means something?

Multiplication is indeed repeated addition.

Mod 0 and Mod 1?

not the first time i saw a joke of "this is just abstract group theory. let's apply it!" *applies it to something abstract as well*

Make the program write code and become sentient

There was a Project Euler problem where I basically had to derive the same steps as in this video, same problem solving approach, and it's neat to see it all in one place, with lots of extra details. Especially if more continued fraction challenges appear.

I like the straight lines that are produced by the output vertices of some cyclotomic polynomials

Converting 2x2 to 5 + 5, adding them and then converting 10 to 4, it's easier than 2x2. You get that? (Definitely for bigger multiplications)

The repeated fractions causes that it might have 2 values.

Just found this channel... Finally motivated to give algebra another go

under adderal I didn't understand a damn thing tomorrow I'll watch it again when my head is clear

I love this channel

Multipliddition.

you lost me at 1:42 "and if we apply that map..." what map? where did you get 12 -> 1 where did you get 5 -> 2 I have no idea what you talking about Left that video at that time

7:53 does that mean you can have mod 117 multiplication on a rubik's cube by assigning edges to thr 12 cycle and corners for the 6 cycle?

6:04 love to see you explain the rubik's cube video in correct scientific terms :)

Haha you used the gdc trick that I told you :)

4:05 I give you two options: use a power of 2 as the clock size and the units are all the odd numbers, or use a prime number as clock size and EVERY number < n is a unit.

Can a mod 100 one exist?

1:05 bruh I was actually thinking that

vvvvvvvvvvu = ?

10³⁰⁰³

-ty is ×10, hundred = ×100

3000ln(10)

(2×2²)(2+1)(4+1)(6+1)(10+1)(12+1)

Does anyone else notice expanding circles?

Oh, you're the rubiks calculator guy. I should subscribble to you

I wonder if anyone has adapted this as an alternative to the current popular blindfold method.

Not even watching this because there is no reason for a 20 minute video on modular arithmetic

Soo if modular multiplication is modular addition then for cpu is possible to add two numbers (8/16/32bit) in CPU and map the sum. Or am I wrong?

"You too is trivial" that was so rude!

you lost me

14:37 if u16 = u2xu4 then u16 = u8, and u32 = u64, and so on. something's wrong here

Ok. But this is a forced distribution. Caveat being there always seems to be a pattern that you may visually lock onto. That’s not much different than looking at them on the number line. Although it is a different way of visualization. Maybe you should be looking at a 4 dimensional representation I don’t know.

Wow that was such a great video, didn't know rubix cubes could go that deep! Now it makes me wonder if this, or a similar concept, could somehow be used by computers, with arithmetic modulo 256, 65536, (all the powers of 2), since right now they still do multiplication the old fashioned way

New sub!

thank you for making these videos. In the youtube sea of AI, sponsored, and low effort atention grab, your videos are a breath of fresh air that really motivate me to think and explore new concepts

Cool video, but it would be really nice to see some applications, like is there a some big prime number, which can represent multiplication of all numbers up to it? I'm very interested in this in terms of speeding up multiplication in processors, can it be used like that?

Tried proving the whole U39 is isomorphic to U35, and all I did was look for generators I don't have a special keyboard so for the purposes of this comment "=" can mean equality, isomorphism, or congruency (whichever is appropriate in context) U39 = U3 × U13. The generator for U3 is 2 but to make it redundant mod 13 it is instead 14. The generator for U13 is 6 but to make it redundant mod 3 it is instead 19. The C12 with generator 19 can be split into a C4 with generator 34 and a C3 with generator 22, with 19 being written as 22_C3 * 34_C4 ^ 3 mod 39. The same can be done with U35 = U5 × U7. U5 = C4 with generator 3, becomes 8 to keep redundancy mod 7. U7 = C6 with generator 3, becomes 31 to keep redundancy mod 5. The C6 with generator 31 is split into C2 with generator 6 and C3 with generator 16, with 31 = 6_C2 * 16_C3 ^ 2 mod 35. The generators are lined up: U39 C2 = 14 || U35 C2 = 6 U39 C3 = 22 || U35 C3 = 16 U39 C4 = 34 || U35 C4 = 8 And now for the final mapping. Take note that this isn't the only way to do this, you could have picked a different set of generators and still get a valid mapping. CYCLES (C2,C3,C4) || U39 || U35 (0,0,0) || 1 || 1 (0,0,1) || 34 || 8 (0,0,2) || 25 || 29 (0,0,3) || 31 || 22 (0,1,0) || 22 || 16 (0,1,1) || 7 || 23 (0,1,2) || 4 || 9 (0,1,3) || 19 || 2 (0,2,0) || 16 || 11 (0,2,1) || 37 || 18 (0,2,2) || 10 || 4 (0,2,3) || 28 || 32 (1,0,0) || 14 || 6 (1,0,1) || 8 || 13 (1,0,2) || 38 || 34 (1,0,3) || 5 || 27 (1,1,0) || 35 || 26 (1,1,1) || 20 || 33 (1,1,2) || 17 || 19 (1,1,3) || 32 || 12 (1,2,0) || 29 || 31 (1,2,1) || 11 || 3 (1,2,2) || 23 || 24 (1,2,3) || 2 || 17

3:30 The text under “1” is top-notch!

Your videos are so confusing lmao

REAL math made by REAL mathematisians

"Wait, it's all clocks?" " *Always has been.* " .

WHY IS NOBODY ELSE CONFUSED T-T

You need to fix your thumbnail, its annoying me, you put 7 and 8 in the mod 6 clock

Oooh... good timing. This might be relevant to the problem I am working on.