Open AccessA GENERALISATION OF THE DIOPHANTINE EQUATION x^2+8∙7^b=y^2r
Author(s) -
Siti Hasana Sapar,
Kai Siong Yow
Publication year - 2021
Publication title -
malaysian journal of science. series b, physical and earth sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 12
ISSN - 1394-3065
DOI - 10.22452/mjs.vol40no2.3
Subject(s) - diophantine equation , mathematics , integral equation , diophantine set , summation equation , legendre's equation , mathematical analysis , pure mathematics , algebra over a field
We investigate the integral solutions to the Diophantine equation where . We first generalise the forms of and that satisfy the equation. We then show the general forms of non-negative integral solutions to the equation under several conditions. We also investigate some special cases in which the integral solutions exist.