Everything you need to know about operations in modular arithmetic

First video ever: • Calculating square roo...
Previous video (LaGrange and Chinese remainder theorem): • Untold connection: Lag...
Congruence relations only work for integers, so can we do division on them? The answer is more complicated than you think - "well no, but actually yes". We need to consider a lot more cases including whether some numbers are coprime.
Note: Most people would learn Euclidean algorithm and its reverse or extension to work out the multiplicative inverse. It is exactly identical to what I have shown here - continued fraction expression is equivalent to Euclidean algorithm; using the property is equivalent to Extended Euclidean algorithm; directly expanding the second-to-last continued fraction convergent is equivalent to Euclidean algorithm in reverse.
Useful link: www.quora.com/...
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#mathemaniac #math #modulararithmetic #division #continuedfraction

[@mathemaniac]

I have been uploading semi-regularly on Friday since the start of the channel, but I don't want to be bound by this "upload schedule" anymore, so new videos are not necessarily uploaded on Friday. Next video will be titled "What is the next term of any sequence?".

[@benYaakov]

I would appreciate if you please provide the link of that video. All the way, Love your vids

[@nigel9637]

amazing explanation, thank you so much

[@eduardvalentin830]

how does this got only 5.6 k views :/. Keep up the work, with this kind of content you will surely get successful!!

[@mathemaniac]

Thanks for the appreciation!

[@brendanmccann5695]

Where is the "previous " video? I only see #1 and #2. This is #1. Good video, though. Thanks.

[@drmathochist06]

Case 1 at 5:11 seems overly complicated. If a and m are coprime, then gcd(a, m) is 1, and b is always divisible by 1!

[@nicoarias9193]

Excellent explanation!

[@mathemaniac]

Thanks!

[@Omar-hm6pu]

Ka=Kb[m] => a=b[m/gcd(m,k)]

[@MrStudent1978]

Could not understand @9:30 ....Could you please clarify...

[@mathemaniac]

This is something I have talked about in my previous videos, namely the first ever video. Don't feel like rehashing the content, so I don't explain in more detail here.

[@dishantpagdar8209]

six