GC1o (Older Version) The Division Algorithm for ordinary Integers

https://youtu.be/tyjF8E2rRHk is a newer better edited version. Watch that instead. When you divide an integer m by another positive integer n, then you get a quotient and a remainder. As long as the remainder is non-negative and less than n, the quotient and the remainder will be unique. This is called "The Division Algorithm" and will be proved rigorously using the Well Ordering Principle. As an example of its use, it is proved that if you square an odd integer and find its remainder when divided by 8, you will always get 1. The Division Algorithm is used in Elementary Number Theory, Elementary Group Theory, and in Ring Theory. One of a series of lectures by Shahriar Shahriari on basic mathematical concepts used in undergraduate college mathematics. Shahriar Shahriari is the William Polk Russell Professor of Mathematics at Pomona College in Claremont, CA USA Shahriari is a 2015 winner of the Mathematical Association of America's Haimo Award for Distinguished Teaching of Mathematics, and six time winner of Pomona College's Wig teaching award.