2021
DOI: 10.7546/nntdm.2021.27.2.88-100
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On the Diophantine equations z^2 = f(x)^2 ± f(x)f(y) + f(y)^2

Abstract: Using the theory of Pell equation, we study the non-trivial positive integer solutions of the Diophantine equations $z^2=f(x)^2\pm f(x)f(y)+f(y)^2$ for certain polynomials f(x), which mean to construct integral triangles with two sides given by the values of polynomials f(x) and f(y) with the intersection angle $120^\circ$ or $60^\circ$.

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Cited by 9 publications
(11 citation statements)
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“…For example, Li et al. demonstrated that the combined application of fibroblast growth factors 2 (FGF2) and LIPU on the OA therapy was superior to FGF2 alone [ 170 ] where the combination of FGF2 and LIPU could both promote the synthesis and secretion of collagen in chondrocytes and induce the differentiation and maturation of chondrocytes during the repair of cartilage defects. Jia et al.…”
Section: Drug Delivery Nanoplatforms Responsive To External Condition...mentioning
confidence: 99%
See 1 more Smart Citation
“…For example, Li et al. demonstrated that the combined application of fibroblast growth factors 2 (FGF2) and LIPU on the OA therapy was superior to FGF2 alone [ 170 ] where the combination of FGF2 and LIPU could both promote the synthesis and secretion of collagen in chondrocytes and induce the differentiation and maturation of chondrocytes during the repair of cartilage defects. Jia et al.…”
Section: Drug Delivery Nanoplatforms Responsive To External Condition...mentioning
confidence: 99%
“…[114] Copyright 2022, Royal Society of Chemistry. application of fibroblast growth factors 2 (FGF2) and LIPU on the OA therapy was superior to FGF2 alone [170] where the combination of FGF2 and LIPU could both promote the synthesis and secretion of collagen in chondrocytes and induce the differentiation and maturation of chondrocytes during the repair of cartilage defects. Jia et al also reported Prussian blue nanoparticle (PB NPs)/LIPUS treatment to be superior to either PB NPs or LIPUS alone in articular cartilage protection.…”
Section: Figurementioning
confidence: 99%
“…The model outputs and validation data (Tang et al., 2023) are available at https://doi.org/10.5281/zenodo.6984180.…”
Section: Data Availability Statementmentioning
confidence: 99%
“…8 For improving the electronical conductivity of rGO in EMI areas, rGO modified with metals, for instance, Ni, Ag, Au, Pt, and Pd have been broadcasted. [9][10][11][12] Among these metals, silver (Ag), owing highest electronic conductivity (6.2 Â 10 7 S/m) was a promising candidate in EMI shielding areas. 13 For example, Tao Long et al one-pot synthesized rGO/Ag compounds through chemical reducing of sodium citrate aided via microwave.…”
Section: Introductionmentioning
confidence: 99%