Special exponential Diophantine equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73614379" target="_blank" >RIV/61989592:15310/22:73614379 - isvavai.cz</a>

Výsledek na webu

<a href="https://obd.upol.cz/id_publ/333194266" target="_blank" >https://obd.upol.cz/id_publ/333194266</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21125/iceri.2022.0270" target="_blank" >10.21125/iceri.2022.0270</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Special exponential Diophantine equations

Popis výsledku v původním jazyce

The article focuses on the specific Diophantine equations, their solution, and the possibility of implementing them in mathematics - competitions, and lessons. High school students should be able to solve various types of Diophantine equations. The article focuses on a particular type of Diophantine equations, their solution, and their introduction to the educational process. Let us mention that the Diophantine equations play an important role in mathematical analysis, especially equation solving. The Diophantine equations are not standard problems in teaching mathematics in high school. However, the current trend is to introduce these non-standard problems into teaching and allow students to explore the solution themselves. Even though the Diophantine equation can be solved using only methods of high school mathematics, during the educational process, it turns out that many students have no idea how to solve problems of the given type. In this contribution, we focus on a specific type of Diophantine equation and solve it using only elementary mathematics. We demonstrate the methods of solution in various mathematical tasks. The paper can be helpful to mathematics teachers who might use it as material in preparing gifted and talented students for mathematical competitions. We would also like to point out the possibility of integrating these problems into the learning process using the help of ICT. The described solution methods can be easily transformed into education in secondary schools. The results can be effortlessly verified within ICT, for example, using the Wolfram Mathematica, or directly visualized using GeoGebra.

Název v anglickém jazyce

Special exponential Diophantine equations

Popis výsledku anglicky

The article focuses on the specific Diophantine equations, their solution, and the possibility of implementing them in mathematics - competitions, and lessons. High school students should be able to solve various types of Diophantine equations. The article focuses on a particular type of Diophantine equations, their solution, and their introduction to the educational process. Let us mention that the Diophantine equations play an important role in mathematical analysis, especially equation solving. The Diophantine equations are not standard problems in teaching mathematics in high school. However, the current trend is to introduce these non-standard problems into teaching and allow students to explore the solution themselves. Even though the Diophantine equation can be solved using only methods of high school mathematics, during the educational process, it turns out that many students have no idea how to solve problems of the given type. In this contribution, we focus on a specific type of Diophantine equation and solve it using only elementary mathematics. We demonstrate the methods of solution in various mathematical tasks. The paper can be helpful to mathematics teachers who might use it as material in preparing gifted and talented students for mathematical competitions. We would also like to point out the possibility of integrating these problems into the learning process using the help of ICT. The described solution methods can be easily transformed into education in secondary schools. The results can be effortlessly verified within ICT, for example, using the Wolfram Mathematica, or directly visualized using GeoGebra.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

50301 - Education, general; including training, pedagogy, didactics [and education systems]

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

ICERI2022 Proceedings

ISBN

978-84-09-45476-1

ISSN

2340-1095

e-ISSN

—

Počet stran výsledku

6

Strana od-do

0920-0925

Název nakladatele

International Association of Technology, Education and Development (IATED)

Místo vydání

Madrid

Místo konání akce

Seville, Španělsko

Datum konání akce

7. 11. 2022

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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