Answered: onsider the theorem: “for any integer…

onsider the theorem: “for any integer x, if x mod 6 = 5, then (x2-2x+4) mod 4 = 3.” (a) Give an outline for a proof of this theorem. (b) Prove this theorem.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.4: Mathematical Induction

Problem 25E

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Question

onsider the theorem: “for any integer x, if x mod 6 = 5, then (x²-2x+4) mod 4 = 3.”
(a) Give an outline for a proof of this theorem.
(b) Prove this theorem.

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