Small prime solutions of a pair of linear equations in five prime variables

Authors
Cui, Zhen Li, Hong Ze
Citation
Cui, Zhen et Li, Hong Ze, Small prime solutions of a pair of linear equations in five prime variables, Acta mathematica Sinica. English series (Print) , 26(3), 2010, pp. 569-578
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
26
Issue
3
Year of publication
2010
Pages
569 - 578
Database
ACNP
SICI code
Abstract
Assume an additional congruent condition on the coefficients. We prove that the pair of linear equations . 5j=1 a .j p j = b . (. = 1, 2) has solutions in primes p j satisfying p j . |b 1| + |b2| +1)max .,j |a .j |2318+.. This improves the exponent 79680 without assuming the additional condition of the second author.s.