Kimberly, I don't know if you are aware of how many lives you've saved hahaha. Just want to appreciate very much your work and hopefully life rewards you back with all the good you have done to too many students!!
@@SawFinMath oh my God ma you just saved me from all the confusion I have been true ,I watched other channel but I was getting more and more confused at the same time but you cleared everything ma your the best may god bless you
For the proof starting at 13:15, I was going to recommend if a congruent to b mod m, then m divides a - b and there exists an integer x such that a - b = mx. Little did I know, you used a much faster formula related to mod, but this proof was in my last test. Thank you for the upload and all of the other great content in this playlist.
The divides relation is a true or false statement. I think it would have been better if you explained in your slide at ~8 min just using the division algorithm instead of the divides relation
hi kimberly i got a question, im very confused on how at 15:39 the division algorithm is b = a + km . so a is the remainder here?? i tried getting there using division by saying okay we have m | (a-b) so a-b = km where k in Z and therefore a = km + b. im still stuck on how you got that division algorithm
clarifying my question a bit more, i got the proof using the way i logically got to the algorithm, so the only question remaining is that we can write any A cong B (mod n) as b = a + kn OR a = b + km ?? in my university definition the def would say ( a>b or a
technically it could be either, K is any integer so it can be positive or negative; b = a - km would be the same as b= a + km. the signs just depend on the k
@@khushisurey1748 where did she get the definition "since a is congruent to b(mod m), then b = a + km) ?? I'm looking through the video but cant find it.
My professor did a practice problem in class for a mod m=b mod m. Using your method it gave me false but my professor got true. The problem was 172 (congruence symbol) 177 (mod 5). Can you please explain again what makes this problem true? What I understood from the video is you determine congruency based on if the remainders are the same.
