e-ISSN 2231-8542
ISSN 1511-3701

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On the Diophantine Equation x2 + 4.7b = y2r

Yow, K. S., Sapar, S. H. and Atan, K. A.

Pertanika Journal of Tropical Agricultural Science, Volume 21, Issue 2, July 2013

Keywords: Diophantine equation, generator, geometric progression

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This paper investigates and determines the solutions for the Diophantine equation x2 + 4.7b = y2r, where x, y, b are all positive intergers and r > 1. By substituting the values of r and b respectively, generators of x and yr can be determined and classified into different categories. Then, by using geometric progression method, a general formula for each category can be obtained. The necessary conditions to obtain the integral solutions of x and y are also investigated.

ISSN 1511-3701

e-ISSN 2231-8542

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