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If p is a natural number, then prove that p"+1 + (p+ 1)2n-1 is divisible by p² + p + 1 for every positive integer n.

If p is a natural number, then prove that p"+1 + (p+ 1)2n-1 is divisible by p² + p + 1 for every positive integer n.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 50E
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If p is a natural number, then prove that pn +1 + (p+ 1)2n-¹ is divisible by p² + p + 1 for every positive integer n.
Transcribed Image Text:If p is a natural number, then prove that pn +1 + (p+ 1)2n-¹ is divisible by p² + p + 1 for every positive integer n.
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