Answered: (c) Theorem: If n is an odd integer,…

(c) Theorem: If n is an odd integer, then 4 divides n-1. n = 2k + 1 n² – 1= (2k + 1)² – 1 = (4k² + 4k + 1) – 1 = 4(k² + k) %3D %3D

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Fill in the words to form a complete proof.

Use the given equations in a complete proof of each theorem. Your proof should be expressed in complete English sentences.

(c) Theorem: If n is an odd integer, then 4 divides n2-1.
n = 2k + 1
n2 – 1 = (2k + 1)² – 1= (4k² + 4k + 1) – 1 = 4(k² + k)

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