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Sur les plus grands facteurs premiers d'entiers consécutifs
- Publication Year :
- 2017
- Publisher :
- HAL CCSD, 2017.
-
Abstract
- Let $P^+(n)$ denote the largest prime factor of the integer $n$ and $P_y^+(n)$ denote the largest prime factor $p$ of $n$ which satisfies $p\leqslant y$. In this paper, firstly we show that the triple consecutive integers with the two patterns $P^+(n-1)>P^+(n)P^+(n+1)$ have a positive proportion respectively. More generally, with the same methods we can prove that for any $J\in \mathbb{Z}, J\geqslant3$, the $J-$tuple consecutive integers with the two patterns $P^+(n+j_0)= \min\limits_{0\leqslant j\leqslant J-1}P^+(n+j)$ and $P^+(n+j_0)= \max\limits_{0\leqslant j\leqslant J-1}P^+(n+j)$ also have a positive proportion respectively. Secondly for $y=x^{\theta}$ with $0<br />Comment: in French
- Subjects :
- 010101 applied mathematics
Combinatorics
Integer
Mathematics - Number Theory
General Mathematics
010102 general mathematics
Prime factor
Integer sequence
0101 mathematics
01 natural sciences
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Mathematics
[MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Subjects
Details
- Language :
- French
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....97b6b08028bce06212692efdd13e1d1c