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(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

(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
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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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)
Transcribed Image Text:(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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