Answered: Prove that for any integers m,n where n…

Prove that for any integers m,n where n > 0 there exists a unique integer 0 ⩽ r < n such that m ≡ r mod n. Since this integer r is unique, we will denote it by m modn

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 32E: 32. Prove that if is an integer, then either or . (Hint: Consider the cases where is even and...

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Prove that for any integers m,n where n > 0 there exists a unique
integer 0 ⩽ r < n such that m ≡ r mod n. Since this integer r is unique, we will denote
it by m modn

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