Decompositions of / into sums and differences of reciprocals of the forms / and /

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F26%3A00566371" target="_blank" >RIV/60162694:G43__/26:00566371 - isvavai.cz</a>
Result on the web
<a href="https://meraa.uniag.sk/docs/2025-01/potucek.pdf" target="_blank" >https://meraa.uniag.sk/docs/2025-01/potucek.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.15414/meraa.2025.11.01.9-17" target="_blank" >10.15414/meraa.2025.11.01.9-17</a>

Result language
angličtina
Original language name
Decompositions of / into sums and differences of reciprocals of the forms / and /
Original language description
This paper addresses the elementary problem of decomposing the reciprocal of a positive integer into a specific sum or difference of two reciprocals and computing their total number. We show that, for any positive integer , the number of decompositions of 1/ into the form 2/±3/ is determined by the number of positive divisors of 6^2, and we derive general results together with explicit formulas. The method is illustrated by explicit decompositions for a chosen positive integer. Finally, we describe a program implemented in the computer algebra system Maple 2025 that computes these decompositions for any positive integer, and we confirm the theoretical results using the earlier example.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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