On the Decompositions of a Reciprocal Into the Sum and the Difference of Two Reciprocals

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F26%3A00566027" target="_blank" >RIV/60162694:G43__/26:00566027 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.iaras.org/home/caijmcm/on-the-decompositions-of-a-reciprocal-into-the-sum-and-the-difference-of-two-reciprocals" target="_blank" >https://www.iaras.org/home/caijmcm/on-the-decompositions-of-a-reciprocal-into-the-sum-and-the-difference-of-two-reciprocals</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On the Decompositions of a Reciprocal Into the Sum and the Difference of Two Reciprocals

Popis výsledku v původním jazyce

This paper deals with the relatively simple problem of determining the decomposition of a reciprocal into the sum or difference of two reciprocals, and of establishing how many such decompositions exist. First, we demonstrate the method on four illustrative cases. We then show that, for a positive integer n, the number of decompositions of 1/n into the sum or difference of two reciprocals is determined by the number of divisors of n2. Afterwards, we illustrate the process of finding decompositions for a specific positive integer. Next, we present the results for an arbitrary positive integer and derive the corresponding explicit formulas. Finally, we present a program created in the computer algebra system Maple 2025 for determining the decompositions for any positive integer, and verify the theoretical results for the previously considered example.

Název v anglickém jazyce

On the Decompositions of a Reciprocal Into the Sum and the Difference of Two Reciprocals

Popis výsledku anglicky

This paper deals with the relatively simple problem of determining the decomposition of a reciprocal into the sum or difference of two reciprocals, and of establishing how many such decompositions exist. First, we demonstrate the method on four illustrative cases. We then show that, for a positive integer n, the number of decompositions of 1/n into the sum or difference of two reciprocals is determined by the number of divisors of n2. Afterwards, we illustrate the process of finding decompositions for a specific positive integer. Next, we present the results for an arbitrary positive integer and derive the corresponding explicit formulas. Finally, we present a program created in the computer algebra system Maple 2025 for determining the decompositions for any positive integer, and verify the theoretical results for the previously considered example.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

International Journal of Mathematical and Computational Methods

ISSN

2367-895X

e-ISSN

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Svazek periodika

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Číslo periodika v rámci svazku

10

Stát vydavatele periodika

BG - Bulharská republika

Počet stran výsledku

9

Strana od-do

231-239

Kód UT WoS článku

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EID výsledku v databázi Scopus

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