hw_06

hw_06 - d ( n ) is odd if and only if n is a perfect...

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Number Theory, Homework 6th batch due: Wednesday, March 11 All exercises are worth 5 points. Please select three problems since there is a cap of 15 points. If you decide to do more than five problems, please indicate which ones you want graded since otherwise the grader will be free to chose problems at will. Exercise 1. 4.2.10: Give an example of a totally multiplicative function f so that F defined by F ( n ) = d | n f ( d ) is not totally multiplicative. Exercise 2. 4.2.12: Show that the number of divisors
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Unformatted text preview: d ( n ) is odd if and only if n is a perfect square. Exercise 3. 4.2.14: For any n , show that there are only finitely many numbers whose divisors add up to n . Exercise 4. 4.3.17: Suppose F and f are related by F ( n ) = ∑ d | n f ( d ) . Show that if F is multiplicative then so is f . (The other direction has been shown in class.) Exercise 5. 4.3.16: Show that f * g is multiplicative if f and g are multiplicative....
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This note was uploaded on 04/05/2010 for the course CS 150 taught by Professor Humphreys,g during the Spring '08 term at UVA.

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