Chinese Remainder Theorem

Рет қаралды 10,278

Prime Newtons

Күн бұрын

Пікірлер: 40

@ArH11117 7 ай бұрын

this explanation was by far the best. literally the best math channel on youtube ❤❤💯💯

@filipkarkalasev 9 ай бұрын

You're an awesome explainer! Thanks a lot.💯

@David-x7u6k 2 ай бұрын

thanks for making this video. your explanation is far better than my CS professor

@francaisdeuxbaguetteiii7316 Жыл бұрын

This is a new concept to me, very good lesson! ❤ May i ask why it doesnt work if the m’s have a common factor? And if they do, is there a way to perhaps change the m so it doesnt share any factors?

@PrimeNewtons Жыл бұрын

The proof is built on the fact that the gcd of the m's is 1. In short. Most theorems in Number Theory are based on this. Someday, I'll do the proof.

@EdmondNzivugira27 3 ай бұрын

Oh my goodness, you're a savior...love you so much

@awoerechinawa9882 11 ай бұрын

Thank you so much your videos were very helpful

@holyshit922 Жыл бұрын

What we did in math for IT class we used extended Euclidean algorithm x = 1(mod 3) x = 2(mod 5) 1=3(2)+5(-1) x = (3*2*2+5*(-1)*1)(mod 15) x = 7 (mod 15) and in second step we have two congruences instead of three x = 7 (mod 15) x = 3 (mod 7) 1 = 15*(1) + 7*(-2) x = (15*1*3 + 7*(-2)*7 ) (mod 105) x = (45 - 98) (mod 105) x = (45 - 98 + 105)(mod 105) x = (45+7)(mod 105) x = 52 (mod 105)

@darcash1738 7 ай бұрын

nice but do u know what was the matrix method he was talking abt?

@matthewpearce940 Ай бұрын

Very good teacher 🎉

@jmoscoso86 2 ай бұрын

What a great explanation!!!

@skwbusaidi 9 ай бұрын

Thank you It is envolve momery I would set x =3a+1 3a+1 =2 ( mod 5) 3a = 1 ( mod 5) The inverse of 3 is 2 a=2 ( mod 5 ) a = 5b +2 Plug a in x x= 3(5b +2)+1 = 15b +7 15b+6 = 3 ( mod 7) 15b = 3 ( mod 7) b = 3 ( mod 7) b = 7c +3 Plug b in x x = 15b+2 = 15(7c+3) +7 = 105c+ 45 + 7 = 105c + 52 Or x = 52 (mod 105)

@SmexiRedditorz 4 ай бұрын

This is gold ! Thanks a lot !

@Blackjag.520 6 күн бұрын

you are my goat brother 🐐

@YonDivi 27 күн бұрын

You're so helpful omg.

@KanjiDenzel 2 ай бұрын

Thanks very much sir I'm looking out for more

@holyshit922 Жыл бұрын

I had it on math for IT class

@yosukesharp 13 күн бұрын

Ty very much boss🙏🏼

@ehanahmed4987 2 ай бұрын

you said we need to break the modulus down to where it has a prime value. how do we do that? (Ex. my question has 8mod12)

@KasperEngineering 26 күн бұрын

12 = 2*2*3 -> factorizing modulus in primes x = 8 (mod 12) becomes: x = 8 (mod 2), and x = 8 (mod 2), and x = 8 (mod 3) note that the first two equations are the same so only need it once x = 8 (mod 2) = 0 (mod 2), and x = 8 (mod 3) = 2 (mod 3)

@JuanLopez-vu7oo 18 күн бұрын

how can someone explain this and be cool at the same time, damn. haha ty!

@ojilesylvester7808 2 ай бұрын

And what if when finding b1 the combo doesn’t have an inverse. What do you do then?

@KasperEngineering 26 күн бұрын

that doesn't happen if all the moduli are coprime. so if it happens, try to adjust the non-coprime moduli, if that's not possible, then there's no valid solution to the system