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On the Riemann hypothesis and the difference between primes
We prove some results concerning the distribution of primes assuming the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval $(x-\frac{4}{\pi} \sqrt{x}...
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On the sum of a prime and a square-free number
We prove that every integer greater than two may be written as the sum of a prime and a square-free number.
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An Explicit Result for Primes Between Cubes
We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.217))$. Our new tool which we derive is a version of Landau's explicit formula for the Riemann zeta-functionExpand
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ON THE NUMBER OF DIVISORS OF $n^{2}-1$
  • A. Dudek
  • Mathematics
  • Bulletin of the Australian Mathematical Society
  • 30 July 2015
We prove an asymptotic formula for the sum $\sum _{n\leq N}d(n^{2}-1)$, where $d(n)$ denotes the number of divisors of $n$. During the course of our proof, we also furnish an asymptotic formula forExpand
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On the Success of Mishandling Euclid's Lemma
Abstract We examine Euclid's lemma that if p is a prime number such that p |ab, then p divides at least one of a or b. Specifically, we consider the common misapplication of this lemma to numbersExpand
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Explicit Estimates in the Theory of Prime Numbers
It is the purpose of this thesis to enunciate and prove a collection of explicit results in the theory of prime numbers. First, the problem of primes in short intervals is considered. We prove thatExpand
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Comparison of Deep Tissue Massage and Therapeutic Massage for Lower Back Pain, Disease Activity, and Functional Capacity of Ankylosing Spondylitis Patients: A Randomized Clinical Pilot Study
Objectives This study aims to compare the effectiveness of deep tissue massage (DTM) and therapeutic massage (TM) in the management of ankylosing spondylitis (AS) patients. Materials and Methods ThisExpand
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On Solving a Curious Inequality of Ramanujan
TLDR
Ramanujan proved that the inequality holds for all sufficiently large values of x. Expand
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Almost-Ramanujan graphs and prime gaps
  • A. Dudek
  • Computer Science, Mathematics
  • Eur. J. Comb.
  • 4 February 2014
The method of Murty and Cioab? shows how one can use results about gaps between primes to construct families of almost-Ramanujan graphs. In this paper we give a simpler construction which avoids theExpand
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Primes in explicit short intervals on RH
On the assumption of the Riemann hypothesis, we give explicit upper bounds on the difference between consecutive prime numbers.
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