2017
DOI: 10.1016/j.jnt.2016.07.024
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On x(ax+ 1)+y(by+ 1)+z(cz+ 1) and x(ax+b)+y(ay+c)+z(az+d)

Abstract: Abstract. In this paper we first investigate for what positive integers a, b, c every nonnegative integer n can be written as x(ax + 1) + y(by + 1) + z(cz + 1) with x, y, z integers. We show that (a, b, c) can be either of the following seven triples

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Cited by 75 publications
(83 citation statements)
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“…pDNA: plasmid DNA; TAT: transactivator of transcription [Color figure can be viewed at wileyonlinelibrary.com] disorders. To determine whether siRNA can be delivered by hPP10, hPP10-E3 (E3, c-terminal double-stranded RNA binding domain from Vaccinia virus [Ostertag, Hoblitzell-Ostertag, & Perrault, 2007]), and TAT-HA-hADR1 (hADR1, double-stranded RNA binding domain from human adenosine deaminase [Sun et al, 2015;Washburn et al, 2014]) fusion protein encoding plasmids were constructed (Supporting Information Figure S3), and the fusion protein was prepared (Figure 6a and 6b). After G418 screening, the GFP-expressing stable Caski cell line was established for further hPP10-mediated siRNA transfection analysis (Supporting Information Figure S4).…”
Section: Hpp10 Mediated Sirna Transfectionmentioning
confidence: 99%
“…pDNA: plasmid DNA; TAT: transactivator of transcription [Color figure can be viewed at wileyonlinelibrary.com] disorders. To determine whether siRNA can be delivered by hPP10, hPP10-E3 (E3, c-terminal double-stranded RNA binding domain from Vaccinia virus [Ostertag, Hoblitzell-Ostertag, & Perrault, 2007]), and TAT-HA-hADR1 (hADR1, double-stranded RNA binding domain from human adenosine deaminase [Sun et al, 2015;Washburn et al, 2014]) fusion protein encoding plasmids were constructed (Supporting Information Figure S3), and the fusion protein was prepared (Figure 6a and 6b). After G418 screening, the GFP-expressing stable Caski cell line was established for further hPP10-mediated siRNA transfection analysis (Supporting Information Figure S4).…”
Section: Hpp10 Mediated Sirna Transfectionmentioning
confidence: 99%
“…In pavement material research, WCO has usually been blended into asphalt to replace or modify the asphalt with improved properties. 14 Some studies have indicated that waste oil can improve the low-temperature performance of asphalt binders and the thermal cracking resistance, [15][16][17] but decrease the rutting resistance of asphalt. [18][19][20][21][22] Existing studies have proved that WCO can be used as an additive in asphalt.…”
Section: Introductionmentioning
confidence: 99%
“…[66] Also, MqsR/MqsA impacts biofilm formation in Pseudomonas fluorescens [67] and impacts persistence and biofilm formation in Pseudomonas putida. [68] In addition, deletion of five TA systems was found to alter biofilm formation by affecting fimbriae production through TabA. [69] Therefore, TA systems have a clear role in biofilm formation.…”
Section: Wwwadv-biosyscom Wwwadvancedsciencenewscommentioning
confidence: 99%