• P-ISSN 0974-6846 E-ISSN 0974-5645

# Indian Journal of Science and Technology

## Article

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Indian Journal of Science and Technology

Year: 2023, Volume: 16, Issue: 28, Pages: 2113-2117

Original Article

## Derivation of Finite Number of Integer Solutions to Particular Form of Mordell’s Equation a2 = b3+r2; r = 8; 9; 10

Received Date:31 May 2023, Accepted Date:18 June 2023, Published Date:22 July 2023

## Abstract

Objectives: The perception of solving Diophantine equations is a massive area of research. Mordell equation is a type of Diophantine equation such that the difference of square and cube of numbers remains constant. Various authors analyses Mordell kind equations for existence of solutions by applying several methods. The objective of this manuscript is whether an equation of the form such that the difference of square and cube of numbers provides square of a particular integer. The possibility of visualization of the surface of the considered equation by using the solutions with the support of MATLAB algorithm is also investigated. Method: Diophantine equations may have infinite number of solutions or finite number of solutions or no solutions in integers. There is no universal method for solving Diophantine equations. The particular type of Mordell’s equation is scrutinized by the concept of divisibility. Findings: A special type of Mordell’s equation such that the difference of square and cube of numbers offers square of a certain integer is inspected by daubing the notions of divisibility. Furthermore, the integer solutions and the corresponding surface of the equation are recognized with the support of MATLAB programs. Novelty: In the analysis, there is no solutions for few cases. The results are confirmed by MATLAB programs. If solutions to the equation exist, the surface of an equation is envisioned with the assistance of MATLAB program.

Keywords: Mordell’s Diophantine Equation; Integer Solutions; Divisibility

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