On the Equation n1n2 = n3n4 Restricted to Factor Closed Sets

Authors
Shi, San Ying Weber, Michel
Citation
Shi, San Ying et Weber, Michel, On the Equation n1n2 = n3n4 Restricted to Factor Closed Sets, Acta mathematica Sinica. English series (Print) , 34(10), 2018, pp. 1517-1530
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
34
Issue
10
Year of publication
2018
Pages
1517 - 1530
Database
ACNP
SICI code
Abstract
We study the number of solutions N(B,F) of the diophantine equation n1n2 = n3n4, where 1 . n1 . B, 1 . n3 . B, n2, n4 . F and F . [1,B] is a factor closed set. We study more particularly the case when F = {m = p.11 · · · p.kk, .j. {0, 1}, 1 . j . k}, p1,..., pk being distinct prime numbers.