On the Decompositions of a Reciprocal Into the Sum and the Difference of Two Reciprocals
The result's identifiers
Result code in 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>
Result on the web
<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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Alternative languages
Result language
angličtina
Original language name
On the Decompositions of a Reciprocal Into the Sum and the Difference of Two Reciprocals
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>ost</sub> - Miscellaneous article in a specialist periodical
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Mathematical and Computational Methods
ISSN
2367-895X
e-ISSN
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Volume of the periodical
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Issue of the periodical within the volume
10
Country of publishing house
BG - BULGARIA
Number of pages
9
Pages from-to
231-239
UT code for WoS article
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EID of the result in the Scopus database
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