| Autor: |
Benfield, Brennan, Lippard, Oliver, Roy, Arindam |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Generalized taxicab numbers are the smallest positive integers that are the sum of exactly $j$, positive $k$-th powers in exactly $m$ distinct ways. This paper is considers for which values of $m$ does a smallest such integer exist as $j$ gets large. There appear to be only two possible outcomes, leading to curious results like there is no positive integer that can be expressed as the sum of exactly $10$ positive squares in exactly $3$ ways. This paper resolves a number of conjectures found in the OEIS by considering generalized Taxicab numbers in the setting of the theory of partitions. |
| Databáze: |
arXiv |
| Externí odkaz: |
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