On a congruence involving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> -Catalan numbers
Ji-Cai Liu
Abstract
Based on a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> -congruence of the author and Petrov, we set up a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> -analogue of Sun–Tauraso’s congruence for sums of Catalan numbers, which extends a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>q</mml:mi> </mml:math> -congruence due to Tauraso.
Topics & Concepts
Congruence (geometry)MathematicsCatalan numberCatalanCongruence relationCombinatoricsPure mathematicsGeometryHumanitiesPhilosophyAdvanced Mathematical IdentitiesAdvanced Combinatorial MathematicsAnalytic Number Theory Research