On the difference of values of the kernel function at consecutive integers
For each positive integer n, set γ(n)=Πp|np. Given a fixed integer k≠±1, we establish that if the ABC-conjecture holds, then the equation γ(n+1)−γ(n)=k has only finitely many solutions. In the particular cases k=±1 , we provide a large family of solutions for each of the corresponding equations....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120330403X |
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| _version_ | 1832565436089106432 |
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| author | Jean-Marie De Koninck Florian Luca |
| author_facet | Jean-Marie De Koninck Florian Luca |
| author_sort | Jean-Marie De Koninck |
| collection | DOAJ |
| description | For each positive integer n, set γ(n)=Πp|np.
Given a fixed integer k≠±1, we establish that if the
ABC-conjecture holds, then the equation
γ(n+1)−γ(n)=k has only finitely many solutions. In
the particular cases k=±1
, we provide a large family of
solutions for each of the corresponding equations. |
| format | Article |
| id | doaj-art-2f6b848fd7c44b46bc25105488bdb032 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2f6b848fd7c44b46bc25105488bdb0322025-02-03T01:07:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003674249426210.1155/S016117120330403XOn the difference of values of the kernel function at consecutive integersJean-Marie De Koninck0Florian Luca1Département de Mathématiques, Université Laval, Québec G1K 7P4, CanadaMathematical Institute, University Nacional Autónoma de México (UNAM), Apartado Postal 61-3 (Xangari), Morelia, Michoacán CP 58 089, MexicoFor each positive integer n, set γ(n)=Πp|np. Given a fixed integer k≠±1, we establish that if the ABC-conjecture holds, then the equation γ(n+1)−γ(n)=k has only finitely many solutions. In the particular cases k=±1 , we provide a large family of solutions for each of the corresponding equations.http://dx.doi.org/10.1155/S016117120330403X |
| spellingShingle | Jean-Marie De Koninck Florian Luca On the difference of values of the kernel function at consecutive integers International Journal of Mathematics and Mathematical Sciences |
| title | On the difference of values of the kernel function at consecutive
integers |
| title_full | On the difference of values of the kernel function at consecutive
integers |
| title_fullStr | On the difference of values of the kernel function at consecutive
integers |
| title_full_unstemmed | On the difference of values of the kernel function at consecutive
integers |
| title_short | On the difference of values of the kernel function at consecutive
integers |
| title_sort | on the difference of values of the kernel function at consecutive integers |
| url | http://dx.doi.org/10.1155/S016117120330403X |
| work_keys_str_mv | AT jeanmariedekoninck onthedifferenceofvaluesofthekernelfunctionatconsecutiveintegers AT florianluca onthedifferenceofvaluesofthekernelfunctionatconsecutiveintegers |