TY - JOUR

T1 - Products in residue classes

AU - Friedlander, John B.

AU - Kurlberg, Pär

AU - Shparlinski, Igor E.

PY - 2008/9

Y1 - 2008/9

N2 - We consider a problem of P. Erdos, A. M. Odlyzko and A. Sárkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results "on average" over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.

AB - We consider a problem of P. Erdos, A. M. Odlyzko and A. Sárkozy about the representation of residue classes modulo m by products of two not too large primes. While it seems that even the Extended Riemann Hypothesis is not powerful enough to achieve the expected results, here we obtain some unconditional results "on average" over moduli m and residue classes modulo m and somewhat stronger results when the average is restricted to prime moduli m = p. We also consider the analogous question wherein the primes are replaced by easier sequences so, quite naturally, we obtain much stronger results.

UR - http://www.scopus.com/inward/record.url?scp=59349120796&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:59349120796

VL - 15

SP - 1133

EP - 1147

JO - Mathematical Research Letters

JF - Mathematical Research Letters

SN - 1073-2780

IS - 5-6

ER -