ON THE QUINARY HOMOGENEOUS BI-QUADRATIC EQUATION x^4 +y^4 -(x+y)w^3=14z^2T^2
DOI:
https://doi.org/10.4314/jfas.v12i2.1Keywords:
Quinary Bi-quadratic Equations, Integer Solutions, Diophantine Equation, Special Sequences.Abstract
The purpose of this paper is to examine the non-zero distinct integral solutions of quinary bi-quadratic homogeneous diophantine equation in integers. In this paper, we present some different patterns of integral solutions to the above diophantine equation in five variables. Also, we obtain some properties as relations between solutions and special numbers.
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References
[1] Bhatia B.L. and Mohanty, S. "Nasty Numbers and Their Characterizations." Mathematical
Education Vol 2(1), 1985, Pp.34-37.
[2] Gopalan M.A., Vidhyalakshmi S., Kavitha A., Premalatha E., On the homogeneous biquadratic
equation with five unknowns 4 4 2 2 2 x y 5 z w R , IAAST, Vol. 4(3), Sep 2013,
37-44.
[3] Gopalan M.A., Vidhyalakshmi S., Premalatha E., On the homogeneous bi-quadratic equation
with five unknowns 4 4 3 x y 8 z w p , IJSRP, Volume-4, Issue-1, January 2014, 1-5.
[4] Gopalan M.A., Vidhyalakshmi S., Maheswari D., Observations on the bi-quadratic equation
with five unknowns 3 3 2 2 2 x y x y 39 w z p , International Journal of
Multidisciplinary Research and Development, Volume-02, Issue-5, May 2015, 83-86.
[5] Gopalan M.A., Kavitha A., Kiruthika R., Observations on the bi-quadratic equation with five
unknowns 3 3 2 2 2 2 2 x y x y 1 3k X Y w , IRJET, Volume-02, Issue-03, June
2015, 1562-1573.s
[6] Gopalan.M.A, Thiruniraiselvi.N, Menaka.P, On the homogeneous bi-quadratic equation with
five unknowns 4 4 3 x y 40 z w p , International Journal of Current Research , Vol.7(07),
, July 2015, Pp.18435-18438.
[7] Gopalan.M.A, Thiruniraiselvi.N, Sridevi.R, Observations on the bi-quadratic equation with five
unknowns 3 3 2 2 2 2 x y 19 z w p , Transactions on Mathematics, Vol.2(1), , January
2016, Pp.01-18
[8] Gopalan M.A., Vidhyalakshmi S., Sumathi G., “Special higher degree Diophantine problems
with solutions”, LAP LAMBERT Academic Publishing, OmniScriptum, Germany, 2017.
[9] Miller, B. "Nasty Numbers." The Mathematics Teacher Vol 73(9), 1980, Pp.649.
[10] Vidhyalakshmi, S., Gopalan, M.A. and Lakshmi, K., Observation on the biquadratic
equation with five unknowns 3 3 2 2 2 2 2 2(x y ) (k 3s )(z w )P , International Journal of
Innovative Research and Review), 2(2), 12-19, June 2014.
[11] Vidhyalakshmi S., Lakshmi K., Gopalan M.A., Integral solution of the bi-quadratic
equation with five unknowns 2 2 2 2 4 x y xy z w zw 5a 3b p , IJIRT, Volume-
1, Issue-10, 2014, 47-52.
[12] Vidhyalakshmi, S., Lakshmi, K. and Gopalan, M.A., Integral solution of the biquadratic
equation with five unknowns 2 2 2 2 4 (x y) xy (z w) zw (5a 3b )P , International Journal of
Innovative Research in Technology, 1(10), 47-52, March 2015.
Education Vol 2(1), 1985, Pp.34-37.
[2] Gopalan M.A., Vidhyalakshmi S., Kavitha A., Premalatha E., On the homogeneous biquadratic
equation with five unknowns 4 4 2 2 2 x y 5 z w R , IAAST, Vol. 4(3), Sep 2013,
37-44.
[3] Gopalan M.A., Vidhyalakshmi S., Premalatha E., On the homogeneous bi-quadratic equation
with five unknowns 4 4 3 x y 8 z w p , IJSRP, Volume-4, Issue-1, January 2014, 1-5.
[4] Gopalan M.A., Vidhyalakshmi S., Maheswari D., Observations on the bi-quadratic equation
with five unknowns 3 3 2 2 2 x y x y 39 w z p , International Journal of
Multidisciplinary Research and Development, Volume-02, Issue-5, May 2015, 83-86.
[5] Gopalan M.A., Kavitha A., Kiruthika R., Observations on the bi-quadratic equation with five
unknowns 3 3 2 2 2 2 2 x y x y 1 3k X Y w , IRJET, Volume-02, Issue-03, June
2015, 1562-1573.s
[6] Gopalan.M.A, Thiruniraiselvi.N, Menaka.P, On the homogeneous bi-quadratic equation with
five unknowns 4 4 3 x y 40 z w p , International Journal of Current Research , Vol.7(07),
, July 2015, Pp.18435-18438.
[7] Gopalan.M.A, Thiruniraiselvi.N, Sridevi.R, Observations on the bi-quadratic equation with five
unknowns 3 3 2 2 2 2 x y 19 z w p , Transactions on Mathematics, Vol.2(1), , January
2016, Pp.01-18
[8] Gopalan M.A., Vidhyalakshmi S., Sumathi G., “Special higher degree Diophantine problems
with solutions”, LAP LAMBERT Academic Publishing, OmniScriptum, Germany, 2017.
[9] Miller, B. "Nasty Numbers." The Mathematics Teacher Vol 73(9), 1980, Pp.649.
[10] Vidhyalakshmi, S., Gopalan, M.A. and Lakshmi, K., Observation on the biquadratic
equation with five unknowns 3 3 2 2 2 2 2 2(x y ) (k 3s )(z w )P , International Journal of
Innovative Research and Review), 2(2), 12-19, June 2014.
[11] Vidhyalakshmi S., Lakshmi K., Gopalan M.A., Integral solution of the bi-quadratic
equation with five unknowns 2 2 2 2 4 x y xy z w zw 5a 3b p , IJIRT, Volume-
1, Issue-10, 2014, 47-52.
[12] Vidhyalakshmi, S., Lakshmi, K. and Gopalan, M.A., Integral solution of the biquadratic
equation with five unknowns 2 2 2 2 4 (x y) xy (z w) zw (5a 3b )P , International Journal of
Innovative Research in Technology, 1(10), 47-52, March 2015.
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Published
2020-03-02
How to Cite
GOPALAN, M. A.; THANGAM, S. A.; OZER, Ö. ON THE QUINARY HOMOGENEOUS BI-QUADRATIC EQUATION x^4 +y^4 -(x+y)w^3=14z^2T^2. Journal of Fundamental and Applied Sciences, [S. l.], v. 12, n. 2, p. 516–524, 2020. DOI: 10.4314/jfas.v12i2.1. Disponível em: https://jfas.info/index.php/JFAS/article/view/741. Acesso em: 30 jan. 2025.
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