Results 41 to 50 of about 496 (82)
What is the smallest prime? [PDF]
, 2012 What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers.
Caldwell, Chris K., Xiong, Yeng
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A Waring–Goldbach type problem for mixed powers
Journal of Number Theory, 2014 Let \(R_4(N)\) denote the number of ways of writing \(N\) in the form \[ N=x^2+p_2^2+p_3^3+p_4^4+p_5^4+p_6^4, \] where \(p_j\)'s are primes and \(x\) is a \(P_6\) (a \(P_r\) means an integer having at most \(r\) prime factors, counted according to multiplicity).
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Waring–Goldbach problem: Two squares and some higher powers
Journal of Number Theory, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Yingjie, Cai, Yingchun
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Mean values of Dirichlet polynomials and applications to linear equations with prime variables
, 2004 We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes.
Angel V. Kumchev +2 more
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Applications of some exponential sums on prime powers: a survey
, 2016 A survey paper on some recent results on additive problems with prime ...
Languasco, Alessandro
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A density version of Waring–Goldbach problem
International Journal of Number TheoryLet [Formula: see text] denote the set of all primes and [Formula: see text] be a positive integer. Suppose that A is a subset of [Formula: see text] with [Formula: see text], where [Formula: see text] is the lower density of A relative to [Formula: see text].
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Some results on Waring-Goldbach type problems
, 2015 This thesis consists of three topics. The first one is on quadratic Waring-Goldbach problems. The second topic is about some additive problems involving fourth powers. The last topic is to consider an average result for the divisor problem in arithmetic progressions. Chapter 1 is an introduction.
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Sylvester: Ushering in the Modern Era of Research on Odd Perfect Numbers
, 2003 In 1888, James Joseph Sylvester (1814-1897) published a series of papers that he hoped would pave the way for a general proof of the nonexistence of an odd perfect number (OPN).
Gimbel, Steven, Jaroma, John
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On the Waring-Goldbach problem on average
, 2018 Let $s$, $\ell$ be two integers such that $2\le s\le \ell-1$, $\ell\ge 3$. We prove that a suitable asymptotic formula for the average number of representations of integers $n=\sum_{i=1}^{s} p_{i}^{\ell}$, where $p_i$, $i=1,\dotsc,s$, are prime numbers, holds in short intervals.
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