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Siemens Westinghouse Competition Math : Science : Technology National Finalist

Siemens Westinghouse Competition Math : Science : Technology National Finalist.

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Siemens Westinghouse Competition Math : Science : Technology National Finalist

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  1. Siemens Westinghouse CompetitionMath : Science : TechnologyNational Finalist • This paper explores the number derivative n', a function defined in terms of the prime factorization of a positive integer n. We find an explicit formula and bounds for the function and investigate how the prime factorizations of n and n' are related. We then extend the function (originally defined only on Z+U{0}) to the rational numbers and find all x in Q + such that x'=0. We prove that the number derivative is discontinuous over all Q+ . Finally, we analyze the equation x =áx for x in Q+ and x in Z+, and find the conditions under which this equation has a solution. • Name: Linda Westrick • High School: Maggie L. Walker Governor’s School for Government and International Studies, Richmond, VA • Mentor: Mr. Pavlo Pylyavskyy • Project Title: Investigations of the Number Derivative

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