| Title |
Divisibility of truncated periodic sequences / |
| Translation of Title |
Nupjautų periodinių sekų dalumas. |
| Authors |
Jonuška, Lukas |
| Full Text |
|
| Pages |
23 |
| Keywords [eng] |
integer parts, expansion in base b, geometric sequences, sveikosios dalys, skaičiaus išraiška bazėje b, geometrinės sekos |
| Abstract [eng] |
A finite set of primes S is called unavoidable with respect to integer b > 1 if and only if for every ξ > 0 the sequence of integers ⌊ξ b^k⌋ contains infinitely many elements divisible by primes from S. It is known that unavoidable sets of primes exist when b = 2, 3, 4, 6 and it does not exist for an integer b > 1 such that b − 1 is square free. If there is no unavoidable set of primes for b, for every finite set of primes S we call its falsifier a real ξ_S > 1 such that the sequence ⌊ξ_S b^k⌋ has only finitely many elements divisible by primes from S. In this paper I classify all b > 1 whose all falsifiers have two ultimately repeating digits. In particular, I show that if b > 3 is prime, then there is no unavoidable set of primes for b. Based on this thesis, I co-authored an article which was published in the International Journal of Number Theory. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Master thesis |
| Language |
English |
| Publication date |
2022 |
