- Tytuł:
- On $B_{2k}$-sequences
- Autorzy:
- Helm, Martin
- Powiązania:
- https://bibliotekanauki.pl/articles/1391772.pdf
- Data publikacji:
- 1993
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Opis:
- Introduction. An old conjecture of P. Erdős repeated many times with a prize offer states that the counting function A(n) of a $B_r$-sequence A satisfies $lim inf_{n→ ∞} (A(n)/(n^{1/r}))=0$. The conjecture was proved for r=2 by P. Erdős himself (see [5]) and in the cases r=4 and r=6 by J. C. M. Nash in [4] and by Xing-De Jia in [2] respectively. A very interesting proof of the conjecture in the case of all even r=2k by Xing-De Jia is to appear in the Journal of Number Theory [3]. Here we present a different, very short proof of Erdős' hypothesis for all even r=2k which we developped independently of Jia's version.
- Źródło:
-
Acta Arithmetica; 1993, 63, 4; 367-371
0065-1036 - Pojawia się w:
- Acta Arithmetica
- Dostawca treści:
- Biblioteka Nauki
Artykuł