3 Proofs of the Multiplication Rule in Modular Arithmetic!

Explanation of 3 different proofs that ac is congruent to bd mod n. The multiplication rule in modular arithmetic is very important for proofs in modular arithmetic!

0:00 First Proof
3:08 Second Proof
5:13 Third Proof

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Music: OcularNebula - The Lopez

[lesnyk]

For whatever reason, modular arithmetic has always sat in a blind spot: I just didn't F***ing get it. Calculus, DiffEq, trig - no problem. Matrices... well, some problem... but congruences? Forget it. But now - a glimmer of light! With your prompting, I worked the 1st of these proofs on my own! A good day is any day you learn something - even at my age (73). Thanks for the push!

[MrCoreyTexas]

I found the third proof the most interesting and creative. How mathematicians figure out what to just "pull out of the ether" in this case adding -bc+bc is really astounding. What separates amateurs like myself from the pros

[ZackSussmanMusic]

super hyped for this series! I really like the first proof, then I would prefer to derive the xp congruent to xq mod n by letting c = d = x in the more general identity

[samaiatraforti]

Another incredible lesson, thankyou so much!! You're a very articulate teacher. So clear and well spoken

[TheAlison]

I give praise, the first proof's Distributive complexity was hidden inside the asterisk. Smart teaching.

[MrCoreyTexas]

So you can multiply both sides of a === b (mod) n by the same number or 2 special congruent numbers of the same n, but not necessarily any old set of numbers.

[mayamirdha]

This is so damn good!
Even tough my teachers couldn't teach me this well like uhh did!
Thnks a lot for this explanation ❤

[TheAlison]

The one thing I don't understand is the adding and multiplying of entire equations. What allows one to do that? It's not a System of Equations, that AFAIU, only permit Addition.

[bigmansanister]

I have a question, is it possible to do a proof by induction with the modular? for example, this equation here where you want to prove that any even number you put in a, c and m will generate even numbers? X=(a*n+c) mod m

[pravallikasegu]

Hi sir, instead of -bc+bc, can we take -ab+ab