Use mathematical induction to prove each of the following: * (a) For each natural number n, 3 divides (4" - 1). (b) For each natural number n, 6 divides (n³ − n).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 51E
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mathematical induction to prove each of the following:
* (a) For each natural number n, 3 divides (4" - 1).
(b) For each natural number n, 6 divides (n³ − n).
Transcribed Image Text:Use mathematical induction to prove each of the following: * (a) For each natural number n, 3 divides (4" - 1). (b) For each natural number n, 6 divides (n³ − n).
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