Congruences from $q$-Catalan Identities

Abstract

In this paper‎, ‎by studying three $q$-Catalan identities given by Andrews‎, ‎we arrive at a certain number of congruences‎. ‎These congruences are all modulo $Phi_n(q)$‎, ‎the $n$-th cyclotomic polynomial or the related functions and modulo $q$-integers‎.

Keywords

• ‎Congruences‎
• ‎$q$-Catalan identities‎
• ‎Catalan numbers‎
• ‎$q$-integer‎
• ‎Cyclotomic polynomial