6. For each of the following conjectures, determine what method of proof would be the most efficient method for proving the statement. You need not write a formal proof (though you can) but you must give an expla- nation for why the method you chose would be most efficient. (a) Given an integer x greater than 2 such that 2³ - 2² +1 is even, prove that the x-th power of the x-th prime is always odd. (b) Prove that if x is a positive integer such that r/log(x) > In(x), then r³ + x>r² - r.

6. For each of the following conjectures, determine what method of proof would be the most efficient method for proving the statement. You need not write a formal proof (though you can) but you must give an expla- nation for why the method you chose would be most efficient. (a) Given an integer x greater than 2 such that 2³ - 2² +1 is even, prove that the x-th power of the x-th prime is always odd. (b) Prove that if x is a positive integer such that r/log(x) > In(x), then r³ + x>r² - r.

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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