This study aims to highlight the importance of knowing the methods of solving Diophantine equations. The material is structured into: Introduction, Classes of Diophantine equations, presentation of first-degree Diophantine equations, Pythagorean triples and higher - Diophantine equations, methods for solving Diophantine equations. The paper describes and exemplifies different methods such as the decomposition method, the parametric method for solving Diophantine equations, solving Diophantine equations with inequalities through the method of modular arithmetic, mathematical induction, Fermat's method of infinite descent. Solving problems is illustrated by various applications of the mathematical results methods presented above. Any education, including mathematical education, has a double effect. On the one hand, the learner gains knowledge, on the other hand, he builds those skills which are engaged in work, develop the abilities needed to perform this education. Mathematical education builds thought. Of course, other actions are involved in building thought, but the role of Mathematical education is essential. This article is part of an empirical research on the teaching and learning of mathematics, teaching practices related to the main classes of Diophantine equations, leading to the development of cognitive skills in students.
| Published in | Science Journal of Education (Volume 2, Issue 1) |
| DOI | 10.11648/j.sjedu.20140201.14 |
| Page(s) | 22-32 |
| 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), 2014. Published by Science Publishing Group |
Diophantine Equations, Linear Equations, Pythagorean Equations, Bachet Equations
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APA Style
Lupu Costică. (2014). Methods of Solving Diophantine Equations in Secondary Education in Romania. Science Journal of Education, 2(1), 22-32. https://doi.org/10.11648/j.sjedu.20140201.14
ACS Style
Lupu Costică. Methods of Solving Diophantine Equations in Secondary Education in Romania. Sci. J. Educ. 2014, 2(1), 22-32. doi: 10.11648/j.sjedu.20140201.14
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Download@article{10.11648/j.sjedu.20140201.14,
author = {Lupu Costică},
title = {Methods of Solving Diophantine Equations in Secondary Education in Romania},
journal = {Science Journal of Education},
volume = {2},
number = {1},
pages = {22-32},
doi = {10.11648/j.sjedu.20140201.14},
url = {https://doi.org/10.11648/j.sjedu.20140201.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjedu.20140201.14},
abstract = {This study aims to highlight the importance of knowing the methods of solving Diophantine equations. The material is structured into: Introduction, Classes of Diophantine equations, presentation of first-degree Diophantine equations, Pythagorean triples and higher - Diophantine equations, methods for solving Diophantine equations. The paper describes and exemplifies different methods such as the decomposition method, the parametric method for solving Diophantine equations, solving Diophantine equations with inequalities through the method of modular arithmetic, mathematical induction, Fermat's method of infinite descent. Solving problems is illustrated by various applications of the mathematical results methods presented above. Any education, including mathematical education, has a double effect. On the one hand, the learner gains knowledge, on the other hand, he builds those skills which are engaged in work, develop the abilities needed to perform this education. Mathematical education builds thought. Of course, other actions are involved in building thought, but the role of Mathematical education is essential. This article is part of an empirical research on the teaching and learning of mathematics, teaching practices related to the main classes of Diophantine equations, leading to the development of cognitive skills in students.},
year = {2014}
}
TY - JOUR T1 - Methods of Solving Diophantine Equations in Secondary Education in Romania AU - Lupu Costică Y1 - 2014/03/10 PY - 2014 N1 - https://doi.org/10.11648/j.sjedu.20140201.14 DO - 10.11648/j.sjedu.20140201.14 T2 - Science Journal of Education JF - Science Journal of Education JO - Science Journal of Education SP - 22 EP - 32 PB - Science Publishing Group SN - 2329-0897 UR - https://doi.org/10.11648/j.sjedu.20140201.14 AB - This study aims to highlight the importance of knowing the methods of solving Diophantine equations. The material is structured into: Introduction, Classes of Diophantine equations, presentation of first-degree Diophantine equations, Pythagorean triples and higher - Diophantine equations, methods for solving Diophantine equations. The paper describes and exemplifies different methods such as the decomposition method, the parametric method for solving Diophantine equations, solving Diophantine equations with inequalities through the method of modular arithmetic, mathematical induction, Fermat's method of infinite descent. Solving problems is illustrated by various applications of the mathematical results methods presented above. Any education, including mathematical education, has a double effect. On the one hand, the learner gains knowledge, on the other hand, he builds those skills which are engaged in work, develop the abilities needed to perform this education. Mathematical education builds thought. Of course, other actions are involved in building thought, but the role of Mathematical education is essential. This article is part of an empirical research on the teaching and learning of mathematics, teaching practices related to the main classes of Diophantine equations, leading to the development of cognitive skills in students. VL - 2 IS - 1 ER -
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