To unlock this lesson you must be a Study.com Member. Number theory is the study of properties of the integers. © copyright 2003-2020 Study.com. All rights reserved. It states that for any integer a and any positive integer b, there exists unique integers q and r such that a = bq + r, where r is greater than or equal to 0 and less than b. 's' : ''}}. 1. You realize this is a simple division problem. You sit down to figure out how many pieces of candy each worker will receive. Pretty cool, huh? An error occurred trying to load this video. succeed. The total number of times b was subtracted from a is the quotient, and the number r is the remainder. All other trademarks and copyrights are the property of their respective owners. Need an assistance with a specific step of a specific Division Algorithm proof. Log in or sign up to add this lesson to a Custom Course. | {{course.flashcardSetCount}} Once armed with Euclid’s algorithm, we can easily compute divisions modulo \(n\). The Division Algorithm is actually a statement about only one variable q. (Division Algorithm) Given integers aand d, with d>0, there exists unique integers qand r, with 0 r

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