Prove the following statement. The difference of any two odd integers is even. Proof: Let m and n be any odd integers. By definition of odd, there are integersr and s so that m can be expressed in terms of r andn can be expressed in terms of s as follows. m = n = Write m - n in terms ofr and s and factor out a 2 to obtain m - n = Now is an integer because differences V of integers are integers. Therefore, m - n = 2: (an integer), and so m - n is even by definition of even Need Help? Read It Watch It

Prove the following statement. The difference of any two odd integers is even. Proof: Let m and n be any odd integers. By definition of odd, there are integersr and s so that m can be expressed in terms of r andn can be expressed in terms of s as follows. m = n = Write m - n in terms ofr and s and factor out a 2 to obtain m - n = Now is an integer because differences V of integers are integers. Therefore, m - n = 2: (an integer), and so m - n is even by definition of even Need Help? Read It Watch It

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 28E: Let and be positive integers. If and is the least common multiple of and , prove that . Note...

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