Some Diophantine equations and inequalities with primes
نویسندگان
چکیده
We consider the solutions to inequality \[|p_1^c + \cdots p_s^c - R| < R^{-\eta}\] (where $c > 1$, \not\in \mb N$ and $\eta$ is a small positive number; $R$ large). obtain new ranges of $c$ for which this has many in primes $p_1, \ldots, p_s$, $s = 2$ (and `almost all' $R$), $s=3$, 4 and~5. also equation integer parts \[[p_1^c] [p_s^c] r\] where $r$ large. Again $c> $c\not\in N$. primes, $s=3$ 5.
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2021
ISSN: ['0208-6573', '2080-9433']
DOI: https://doi.org/10.7169/facm/1912