Bound on some Diophantine equation

Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper will concentrate on finding the least upper bound to the Diophantine equation x 2 + 2a 7 b = y n for 1 ≤ α ≤ 8 and found that there exists an integral solution to the...

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Main Authors: Amalulhair, N. H., Sapar, S. H., Johari, M. A. M.
Format: Article
Published: Malaysian Mathematical Sciences Society 2022
Online Access:http://psasir.upm.edu.my/id/eprint/100565/
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author Amalulhair, N. H.
Sapar, S. H.
Johari, M. A. M.
author_facet Amalulhair, N. H.
Sapar, S. H.
Johari, M. A. M.
author_sort Amalulhair, N. H.
building UPM Institutional Repository
collection Online Access
description Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper will concentrate on finding the least upper bound to the Diophantine equation x 2 + 2a 7 b = y n for 1 ≤ α ≤ 8 and found that there exists an integral solution to the equation for y = 2 and y > 2 with the bound on n < 15,000 and n < 11,000 respectively.
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institution Universiti Putra Malaysia
institution_category Local University
last_indexed 2025-11-15T13:31:38Z
publishDate 2022
publisher Malaysian Mathematical Sciences Society
recordtype eprints
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spelling upm-1005652023-10-10T02:13:08Z http://psasir.upm.edu.my/id/eprint/100565/ Bound on some Diophantine equation Amalulhair, N. H. Sapar, S. H. Johari, M. A. M. Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper will concentrate on finding the least upper bound to the Diophantine equation x 2 + 2a 7 b = y n for 1 ≤ α ≤ 8 and found that there exists an integral solution to the equation for y = 2 and y > 2 with the bound on n < 15,000 and n < 11,000 respectively. Malaysian Mathematical Sciences Society 2022-07-29 Article PeerReviewed Amalulhair, N. H. and Sapar, S. H. and Johari, M. A. M. (2022) Bound on some Diophantine equation. Menemui Matematik (Discovering Mathematics), 44 (1). 28 - 34. ISSN 0126-9003 https://myjms.mohe.gov.my/index.php/dismath/article/view/18943
spellingShingle Amalulhair, N. H.
Sapar, S. H.
Johari, M. A. M.
Bound on some Diophantine equation
title Bound on some Diophantine equation
title_full Bound on some Diophantine equation
title_fullStr Bound on some Diophantine equation
title_full_unstemmed Bound on some Diophantine equation
title_short Bound on some Diophantine equation
title_sort bound on some diophantine equation
url http://psasir.upm.edu.my/id/eprint/100565/
http://psasir.upm.edu.my/id/eprint/100565/