Geodesic
On $B_{2k}$-sequences
Acta Arithmetica, Tome 63 (1993) no. 4, pp. 367-371.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa-63-4-367-371

Martin Helm 1

1 
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Martin Helm. On $B_{2k}$-sequences. Acta Arithmetica, Tome 63 (1993) no. 4, pp. 367-371. doi : 10.4064/aa-63-4-367-371. http://geodesic.mathdoc.fr/articles/10.4064/aa-63-4-367-371/

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