Mastering Modular Arithmetic Operations: The Complete Guide 📘

First video ever: https://youtu.be/oOsYACy0UUY
Previous video (LaGrange and Chinese remainder theorem): https://youtu.be/iIV9tdmWYmU

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: https://www.quora.com/q/igcnjlpcjdmjyiqa/Chinese-a-remarkable-achievement-in-modular-arithmetic

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If you want to know more interesting Mathematics, stay tuned for the next video!

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#mathemaniac #math #modulararithmetic #division #continuedfraction