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- W4289244021 abstract "Let $b$ be a numeration base. A $b$-additive Ramanujan-Hardy number $N$ is an integer for which there exists at least an integer $M$, called additive multiplier, such that the product of $M$ and the sum of base $b$ digits of $N$, added to the reversal of the product, gives $N$. We show that for any $b$ there exists an infinity of $b$-additive Ramanujan-Hardy numbers and an infinity of additive multipliers. A $b$-multiplicative Ramanujan-Hardy number $N$ is an integer for which there exists at least an integer $M$, called multiplicative multiplier, such that the product of $M$ and the sum of base $b$ digits of $N$, multiplied by the reversal of the product, gives $N$. We show that for an even $b$, $bequiv 1 pmod {3}$, and for $b=2$, there exists an infinity of $b$-multiplicative Ramanujan-Hardy numbers and an infinity of multiplicative multipliers. These results completely answer two questions and partially answer two other questions among those asked in V. Nic{t}icu{a}, emph{About some relatives of the taxicab number}, arXiv:1805.10739v4." @default.
- W4289244021 created "2022-08-01" @default.
- W4289244021 creator A5007419318 @default.
- W4289244021 date "2018-11-25" @default.
- W4289244021 modified "2023-10-17" @default.
- W4289244021 title "Infinite sets of $b$-additive and $b$-multiplicative Ramanujan-Hardy numbers" @default.
- W4289244021 doi "https://doi.org/10.48550/arxiv.1811.10035" @default.
- W4289244021 hasPublicationYear "2018" @default.
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