On The Existence of Prime Numbers in Polynomial Sequences, And Odd Perfect Numbers
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Date
2015-06
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Publisher
University Of Ghana
Abstract
It is known that certain polynomials of degree one, with integer coefficients,
admit in nitely-many primes. In this thesis, we provide an alternative proof
of Dirichlets theorem concerning primes in arithmetic progressions, without
applying methods involving Dirichlet characters or the Riemann Zeta func-
tion. A more general result concerning multiples of primes in short-intervals
is also provided.
This thesis also considers problems concerning the existence of odd perfect
numbers. The main contribution is a good upper-bound on the largest prime
divisor of an odd perfect number. In addition, we show how new results
concerning odd perfect numbers or k - perfect numbers can be obtained by
applying a property of completely-multiplicative functions.
Description
Thesis(PhD)- University Of Ghana, 2015
Keywords
Prime Numbers, Polynomial Sequence, Odd Perfect Number