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O If a and b are positive integers with a < b, then ua(1) < up(1) for all t 0.

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 24E: Let (a,b)=1. Prove that (a,bn)=1 for all positive integers n.

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Question

decide if the given statement is true or false,and give a brief justiﬁcation for your answer.If true, you can quote a relevant deﬁnition or theorem . If false,provide an example,illustration,or brief explanation of why the statement is false.

O If a and b are positive integers with a < b, then
ua(1) < up(1) for all t 0.

Expert Solution

Step 1

The unit step function defined as,

Similarly,

The rectangular unit step function is defined as,

If a < b,

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