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)
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)
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?
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this explanation was by far the best. literally the best math channel on youtube ❤❤💯💯
You're an awesome explainer! Thanks a lot.💯
Oh my goodness, you're a savior...love you so much
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)
nice but do u know what was the matrix method he was talking abt?
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)
Thank you so much your videos were very helpful
This is gold ! Thanks a lot !
No doubt remains that we need Prime Newtons! 😊🎉
As far as Chinese inventions go the CRT ranks right along side Kung Pao Chicken AFAIAC. 😋
Had to Google Kung Pao Chicken 🤣
❤❤❤❤@@PrimeNewtonsI am an Olimpiad student in Ghana and I like your lessons a lot
Great!
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?
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.
I had it on math for IT class
👍👍👍👍👍👍👍👍👍👍👍👍very good
I thought if critical race theory when I saw CRT
Thanks man
W video
man ❤
what does b and c represent
Did you watch the video?
@@PrimeNewtons i did, but I'm a bit slow lol
at 4 mins into the video 4:36