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On the least common multiple of polynomial sequences at prime arguments.
- Source :
- International Journal of Number Theory; Jul2022, Vol. 18 Issue 6, p1227-1237, 11p
- Publication Year :
- 2022
-
Abstract
- Cilleruelo conjectured that if f ∈ ℤ [ x ] is an irreducible polynomial of degree d ≥ 2 then, log lcm { f (n) | n < x } ∼ (d − 1) x log x. In this paper, we investigate the analog of prime arguments, namely, lcm { f (p) | p < x } , where p denotes a prime and obtain nontrivial lower bounds on it. Further, we also show some results regarding the greatest prime divisor of f (p). [ABSTRACT FROM AUTHOR]
- Subjects :
- POLYNOMIALS
ARGUMENT
IRREDUCIBLE polynomials
Subjects
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 18
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 157269685
- Full Text :
- https://doi.org/10.1142/S1793042122500622