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On the system of double equations with three unknowns $d+ay+bx+cx^2=z^2 , y+z=x^2$ | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 45، دوره 12، شماره 1، مرداد 2021، صفحه 575-581 اصل مقاله (327.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.4840 | ||
| نویسندگان | ||
| Mayilrangam Gopalan1؛ Aarthy Thangam1؛ Ozen Ozer* 2 | ||
| 1Department of Mathematics, Shrimati Indira Gandhi College, Trichy-620 002, Tamil Nadu, India | ||
| 2Department of Mathematics, Faculty of Science and Arts, Kirklareli University, 39100, Kirklareli, Turkey | ||
| تاریخ دریافت: 18 فروردین 1397، تاریخ بازنگری: 09 مرداد 1398، تاریخ پذیرش: 25 مهر 1398 | ||
| چکیده | ||
| The system of double equations with three unknowns given by $d+ay+bx+cx^2=z^2 , y+z=x^2$ is analysed for its infinitely many non-zero distinct integer solutions. Different sets of integer solutions have been presented. A few interesting relations among the solutions are given. | ||
| کلیدواژهها | ||
| System of double equations؛ Pair of equations with three unknowns؛ Integer solutions؛ Pell Equations؛ Special Numbers | ||
| مراجع | ||
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[1] L.E. Dickson, History of the Theory of Numbers, Vol. II, Chelsea Publishing Company, New York, 1952. [2] B. Batta and A.N. Singh, History of Hindu Mathematics, Asia Publishing House, 1938. [3] M.A. Gopalan and S. Devibala, Integral solutions of the double equations x(y−k)=v2, y(x−h)=u2, IJSAC 1(1) (2004) 53–57. [4] M.A. Gopalan and S. Devibala, On the system of double equations x2−y2+N=u2, x2−y2-N =v2, Bull. Pure Appl. Sci. 23(2) (2004) 279–280. [5] M.A. Gopalan and S. Devibala, Integral solutions of the system a(x2−y2)+N12=u2, b(x2−y2)+N22 =v2, Acta Ciencia Indica XXXIM(2) (2005) 325–326. [6] M.A. Gopalan and S. Devibala, Integral solutions of the system x2−y2+b=u2, a(x2−y2)+c =v2, Acta Ciencia Indica XXXIM(2) (2005) 607. [7] M.A. Gopalan and S. Devibala, On the system of binary quadratic diophantine equations a(x2−y2)+N=u2 b(x2−y2)+N=v2, Pure Appl. Math. Sci. LXIII(1-2) (2006) 59–63. [8] M.A. Gopalan, S. Vidhyalakshmi and K. Lakshmi, On the system of double equations 4x2−y2 = z2, x2+2y2= w2, Scholars J. Engin. Technol. 2(2A) (2014) 103–104. [9] M.A. Gopalan, S. Vidhyalakshmi and R. Janani, On the system of double Diophantine equations a0+a1=q2, a0a1±2(a0+a1) =p2 −4, Trans. Math. 2(1) (2016) 22–26. [10] M.A. Gopalan, S. Vidhyalakshmi and A. Nivetha, On the system of double Diophantine equations a0+a1=q2, a0a1± 6(a0 + a1)= p2−36, Trans. Math. 2(1) (2016) 41–45. [11] M.A. Gopalan, S. Vidhyalakshmi and E. Bhuvaneswari, On the system of double Diophantine equations a0+a1=q2, a0a1± 4(a0 + a1)= p2−16, Jamal Acad. Res. J. Special Issue, 2016, 279–282. [12] K. Meena, S. Vidhyalakshmi and C. Priyadharsini, On the system of double Diophantine equations a0+a1=q2, a0a1± 5(a0 + a1)=p2−25, Open J. Appl. Theor. Math. 2(1) (2016) 8–12. [13] M.A. Gopalan, S. Vidhyalakshmi and A. Rukmani, On the system of double Diophantine equations a0−a1=q2, a0a1±(a0−a1)=p2 + 1, Trans. Math. 2(3) (2016) 28–32. [14] S. Devibala, S. Vidhyalakshmi, G. Dhanalakshmi, On the system of double equations N1−N2=4k+2 (k >0), N1N2 (2k+1) α2, Int. J. Engin. Appl. Sci. 4(6) (2017) 44–45. | ||
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