Browsing by Author "Guloglu, Ahmet M."
Now showing 1 - 2 of 2
- Results Per Page
- Sort Options
Article Citation Count: 1Cyclicity of elliptic curves modulo primes in arithmetic progressions(Cambridge Univ Press, 2022) Akbal, Yıldırım; Guloglu, Ahmet M.; MathematicsWe 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 Citation Count: 0Variations on a theme of Mirsky(World Scientific Publ Co Pte Ltd, 2023) Akbal, Yıldırım; Guloglu, Ahmet M.; MathematicsLet 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.