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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This is Discrete Math. Please show all work and give explanations for solutions. Thank you!

Transcribed Image Text: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 2³-²+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 r¹/log(x) > In(x),
then x³ + x>x² - x.
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