Everything you need to know about operations in modular arithmetic

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 Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! #mathemaniac #math #modulararithmetic #division #continuedfraction