On a question of Luca and Schinzel over Segal–Piatetski-Shapiro sequences

نویسندگان

چکیده

We extend to Segal–Piatetski-Shapiro sequences previous results on the Luca–Schinzel question. Namely, we prove that for any real c larger than 1, sequence $$(\sum _{m\le n} \varphi (\lfloor m^c \rfloor ) /\lfloor )_{n\ge 1}$$ is dense modulo where $$\varphi $$ denotes Euler’s totient function. The main part of proof consists in showing when R a large integer, residues $$\lfloor contains block consecutive given length.

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ژورنال

عنوان ژورنال: Ramanujan Journal

سال: 2022

ISSN: ['1572-9303', '1382-4090']

DOI: https://doi.org/10.1007/s11139-022-00684-z