On x3 + y3 = D

Chowla, S.; Cowles, John; Cowles, Mary Jane

doi:10.1016/0022-314x(82)90072-5

Cited by 5 publications

(4 citation statements)

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“…For example, the equation x 5 + y 5 = u 5 + v 5 has no known nontrivial solution and it is expected that x 5 + y 5 = n has O(1) integer solutions for any n ∈ N . (Note that x 3 + y 3 = n has an unbounded number of solutions [3]. )…”

Section: Higher Powersmentioning

confidence: 99%

The Uniformity Conjecture in Additive Combinatorics

Shkredov¹,

Solymosi²

2020

Preprint

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Section: Higher Powersmentioning

confidence: 99%

The Uniformity Conjecture in Additive Combinatorics

Shkredov¹,

Solymosi²

2020

Preprint

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“…We have investigated this for a number of compounds and in some cases have been successful in removing the sample matrix without losing the analytes of interest. An example of this approach is the sample preparation and analysis of chlorosilanes (5). It was found that metal contaminants in dichlorosilane (DCS), which is a gas at ambient temperature, can be quantified by decomposing the DCS in an aqueous solution of HF.…”

Section: Matrix Removal During Sample Preparationmentioning

confidence: 99%

Analytical Characterization of ALD Thin Film Precursors

et al. 2010

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Moore's Law compliance necessitates the use of high dielectric constant (k) (e.g. Hf, Ti, Zr, Ta) and low-k (e.g. silane chemistries) material thin films in place of traditional Si/SiO2 films. Chemical precursors of these films require characterization of trace-level impurities to avoid device failure. The reporting limits listed on precursor Certificates of Analysis require analytical methods such as inductively coupled plasma - mass spectrometry (ICP-MS) ion chromatography (IC) and gas chromatography - mass spectrometry (GC-MS), for determination of trace elements, chloride and precursor purity, respectively. Analytical challenges associated with characterizing these materials include precursor volatility, air and moisture sensitivity, parent element ICP-MS matrix effects and ICP-MS elemental and molecular interferences. In addition, sample preparation methods preceding the analyses must decompose the sample yet preserve the integrity and quantity of the analytes present in the original samples. This paper will describe analytical methods designed to meet these analytical challenges.

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“…The literature contains a very large number of articles on non-linear such individual equations involving primes and powers of all kinds. Among them are for example [1,4,5,6].…”

Section: Introductionmentioning

confidence: 99%

On Solutions of the Diophantine Equations p^3 + q^3 = z^2 and p^3 - q^3 = z^2 when p, q are Primes

Burshtein¹

2018

APAM

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In this paper, we consider the two equations p 3 + q 3 = z 2 and p 3-q 3 = z 2 when p, q are primes. Among the various results attained, it is shown that both equations have no solutions when q = 2, and z 2 is a multiple of 9 in each and every solution. In particular, when 3 ≤ q < p ≤ 101, all the possibilities for solutions of each equation are examined for all primes p, q. It is established that each equation has exactly one solution which is exhibited. For primes larger than 101, it is presumed that both equations may have additional solutions by using a computer.

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On x3 + y3 = D

Cited by 5 publications

References 0 publications

The Uniformity Conjecture in Additive Combinatorics

The Uniformity Conjecture in Additive Combinatorics

Analytical Characterization of ALD Thin Film Precursors

On Solutions of the Diophantine Equations p^3 + q^3 = z^2 and p^3 - q^3 = z^2 when p, q are Primes

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