Type: Article
Publication Date: 2004-07-01
Citations: 2
DOI: https://doi.org/10.4134/jkms.2004.41.4.717
A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which <TEX>$2^a\;-\;2^b$</TEX> divides <TEX>$n^a\;-\;n^b$</TEX> for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements <TEX>${\alpha}_1,\;{\cdots},\;{{\alpha}_{\kappa}}\;and\;{\beta}$</TEX> in the ring of integers A of a number field for which <TEX>${\Sigma{\kappa}{i=1}}{\alpha}_i{\beta}^{{\alpha}i}\;divides\;{\Sigma{\kappa}{i=1}}{\alpha}_i{z^{{\alpha}i}}\;for\;any\;z\;{\in}\;A$</TEX>. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.
| Action | Title | Year | Authors |
|---|---|---|---|
| + | A generalization of Selfridge's question | 2019 |
Devendra Prasad |
| + PDF Chat | A Survey on Fixed Divisors | 2019 |
Devendra Prasad Krishnan Rajkumar A. Satyanarayana Reddy |