Homogeneous Quartic Equation (x + y)(x^3 + y^3) = kw^2p^2

Abstract-In this research, we applied the idea stemming from the equation (x - y)(x3 + y3) = 4(w2 - p2) to generalize the homogeneous quartic equation (x + y)(x3 + y3) = kw2p2, where k = 3 + n2, n ∈ Z. Through the application of appropriate transformations, it becomes a simplified equation of the fo...

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Bibliographic Details
Published inIAENG international journal of applied mathematics Vol. 53; no. 4; pp. 1 - 9
Main Authors Muthuvel, S, Venkatraman, R
Format Journal Article
LanguageEnglish
Published Hong Kong International Association of Engineers 01.12.2023
Subjects
Mathematical analysis
Quartic equations
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Summary:Abstract-In this research, we applied the idea stemming from the equation (x - y)(x3 + y3) = 4(w2 - p2) to generalize the homogeneous quartic equation (x + y)(x3 + y3) = kw2p2, where k = 3 + n2, n ∈ Z. Through the application of appropriate transformations, it becomes a simplified equation of the form u2 +3v2 = kp2, where varying equations are obtained by altering the values of n. We formulated equations using specific n values such as 4,8,11,13,15,16,17,18,19 and 20. Solving these equations yielded a range of patterns, the solutions of which were determined to be non-zero integral solutions.
ISSN:1992-9978
1992-9986