Results 51 to 60 of about 496 (82)
Cubic Waring-Goldbach problem with Piatetski-Shapiro primes
In this paper, it is proved that, for $γ\in(\frac{317}{320},1)$, every sufficiently large odd integer can be written as the sum of nine cubes of primes, each of which is of the form $[n^{1/γ}]$. This result constitutes an improvement upon the previous result of Akbal and Güloğlu [1].
Long, Linji +3 more
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On the Waring-Goldbach Problem for tenth powers
, 2016 Using sharper Weyl sum estimates, we show that $H(10)\le 105$, improving upon the previous bound of $107$.
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Abstracts of the 2013 Annual Meeting of the American College of Rheumatology. October 25-30, 2013. San Diego, California, USA. [PDF]
Arthritis Rheum, 2013 europepmc +1 more source
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Waring–Goldbach problem involving cubes of primes
Mathematische Zeitschrift, 2020Using the circle method the authors prove two main results: (a) Every sufficiently large integer is a sum of one prime number, four cubes of primes, and fifteen powers of \(2\). Assuming the Riemann hypothesis the number of powers of two is reduced to seven.
Ching, Tak Wing, Tsang, Kai Man
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On Waring–Goldbach problem for unlike powers
International Journal of Number Theory, 2018Let [Formula: see text] denote an almost-prime with at most [Formula: see text] prime factors, counted according to multiplicity. In this paper, it is proved that, for [Formula: see text] and for every sufficiently large even integer [Formula: see text], the equation [Formula: see text] is solvable with [Formula: see text] being an almost-prime ...
Li, Jinjiang, Zhang, Min
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ON WARING–GOLDBACH PROBLEM FOR FIFTH POWERS
International Journal of Number Theory, 2012In this short paper, we investigate exceptional sets in the Waring–Goldbach problem for fifth powers. For example, we show that all but O(N213/214) integers subject to the necessary local conditions can be represented as the sum of 11 fifth powers of primes. This improves the previous result.
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Waring–Goldbach problem: two squares and some unlike powers
Acta Mathematica Hungarica, 2014This paper shows that every sufficiently large odd integer \(N\) may be written as \[ N=x^2+p_2^2+p_3^3+p_4^4+p_5^5+p_6^6+p_7^7, \] in which the \(p_i\) are prime, and \(x\) is a \(P_6\) almost-prime. Indeed this result is one of a range of theorems in which the final term is replaced by \(p_7^k\) for some \(k\in [6,19]\), and \(x\) is a \(P_r\) almost-
Cai, Yingchun, Mu, Quanwu
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