We investigate the interplay between the Chinese Remainder Theorem and the theory of congruent numbers through a modular approach to expressing integers as sums of three cubes. By analyzing congruence systems arising from specific residue classes modulo 8 and modulo 9, we classify the possible integers likely to be representable as sums of cubes based on their modular residues. We also explore computational methods applying this modular framework to identify explicit cube decompositions within these classes.
| Published in | Pure and Applied Mathematics Journal (Volume 14, Issue 5) |
| DOI | 10.11648/j.pamj.20251405.16 |
| Page(s) | 157-160 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2025. Published by Science Publishing Group |
Congruent Numbers, Chinese Remainder Theorem, Modular Arithmetic, Sums of Cubes, Diophantine Equations
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APA Style
Vincent, K. K. (2025). On a Family of Congruent Numbers Defined Modulo 72: A Conjectural Study. Pure and Applied Mathematics Journal, 14(5), 157-160. https://doi.org/10.11648/j.pamj.20251405.16
ACS Style
Vincent, K. K. On a Family of Congruent Numbers Defined Modulo 72: A Conjectural Study. Pure Appl. Math. J. 2025, 14(5), 157-160. doi: 10.11648/j.pamj.20251405.16
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Download@article{10.11648/j.pamj.20251405.16,
author = {Kouakou Kouassi Vincent},
title = {On a Family of Congruent Numbers Defined Modulo 72: A Conjectural Study
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journal = {Pure and Applied Mathematics Journal},
volume = {14},
number = {5},
pages = {157-160},
doi = {10.11648/j.pamj.20251405.16},
url = {https://doi.org/10.11648/j.pamj.20251405.16},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20251405.16},
abstract = {We investigate the interplay between the Chinese Remainder Theorem and the theory of congruent numbers through a modular approach to expressing integers as sums of three cubes. By analyzing congruence systems arising from specific residue classes modulo 8 and modulo 9, we classify the possible integers likely to be representable as sums of cubes based on their modular residues. We also explore computational methods applying this modular framework to identify explicit cube decompositions within these classes.
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year = {2025}
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TY - JOUR T1 - On a Family of Congruent Numbers Defined Modulo 72: A Conjectural Study AU - Kouakou Kouassi Vincent Y1 - 2025/10/22 PY - 2025 N1 - https://doi.org/10.11648/j.pamj.20251405.16 DO - 10.11648/j.pamj.20251405.16 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 157 EP - 160 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20251405.16 AB - We investigate the interplay between the Chinese Remainder Theorem and the theory of congruent numbers through a modular approach to expressing integers as sums of three cubes. By analyzing congruence systems arising from specific residue classes modulo 8 and modulo 9, we classify the possible integers likely to be representable as sums of cubes based on their modular residues. We also explore computational methods applying this modular framework to identify explicit cube decompositions within these classes. VL - 14 IS - 5 ER -
Applied Fundamental Sciences Department, Nangui Abrogoua University, Abidjan, Côte d’Ivoire
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