Prove the following statement P(n) by weak mathematical induction: 22n – 1 is divisible by 3, for each integer n > 0 - (Direction: State the basis step, inductive hypothesis, inductive step, and conclusion clearly.)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 35E
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Prove the following statement P(n) by weak mathematical induction:
22n – 1 is divisible by 3, for each integer n > 0
(Direction: State the basis step, inductive hypothesis, inductive step, and conclusion clearly.)
Transcribed Image Text:Prove the following statement P(n) by weak mathematical induction: 22n – 1 is divisible by 3, for each integer n > 0 (Direction: State the basis step, inductive hypothesis, inductive step, and conclusion clearly.)
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Step 1

P(n) : 22n - 1 is divisible by 3 , for each integer n>=0 

We prove this by method of induction.

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