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Article Citation - WoS: 1Citation - Scopus: 1A Short Note on Some Arithmetical Properties of the Integer Part of Ap(Tubitak Scientific & Technological Research Council Turkey, 2019) Akbal, YıldırımLet $a>0$ be an irrational number. We study some of the arithmetical properties of ${\\{\\lfloor ap\\rfloor\\}}_{p=2}^\\infty$ where pdenotes a prime number and $\\lfloor x\\rfloor$ denotes the largest integer not exceeding x.Article Citation - WoS: 5Citation - Scopus: 4Cyclicity of Elliptic Curves Modulo Primes in Arithmetic Progressions(Cambridge University Press, 2022) Akbal,Y.; Güloǧlu,A.M.We consider the reduction of an elliptic curve defined over the rational numbers modulo primes in a given arithmetic progression and investigate how often the subgroup of rational points of this reduced curve is cyclic. ©Article Variations on a Theme of Mirsky(World Scientific, 2023) Akbal,Y.; Güloǧlu,A.M.Let k and r be non-zero integers with r ≥ 2. An integer is called r-free if it is not divisible by the rth power of a prime. A result of Mirsky states that there are infinitely many primes p such that p + k is r-free. In this paper, we study an additive Goldbach-type problem and prove two uniform distribution results using these primes. We also study certain properties of primes p such that p + a1,...,p + aℓ are simultaneously r-free, where a1,...,aℓ are non-zero integers and ℓ ≥ 1. © 2023 World Scientific Publishing Company.
