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