Comptes Rendus
no. 9-10
Number Theory
On Zarembaʼs conjecture
Presented by: Jean Bourgain
Jean Bourgain1; Alex Kontorovich2
1IAS, Princeton, NJ 08540, USA
2Stony Brook University, Stony Brook, NY 11794, USA
Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 493-495

It is shown that there is a constant A and a density one subset S of the positive integers such that, for each q∈S, there is some 1⩽p<q, (p,q)=1, so that pq has all its partial quotients bounded by A.

On montre quʼil existe une constante A et un sous-ensemble S des entiers positifs de densité un, tel que pour tout q∈S il y a un entier 1⩽p<q,(p,q)=1 pour lequel les quotients partiels de pq sont bornés par A.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.03.023

Jean Bourgain  1 ; Alex Kontorovich  2

1 IAS, Princeton, NJ 08540, USA
2 Stony Brook University, Stony Brook, NY 11794, USA 
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Jean Bourgain; Alex Kontorovich. On Zarembaʼs conjecture. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 493-495. doi: 10.1016/j.crma.2011.03.023

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