A Note on the \(q\)-Lucas Theorem

Xiang Gao1,2
1ScHOOL OF MATHEMATICAL SCIENCES, OCEAN UNIVERSITY OF CHINA, LANE 238, Sonciine Roap, LaosHan District, Qivcpao City, SHANDONG PROVINCE, 266100, PEOPLE’s REPUBLIC OF CHINA.
2DEPARTMENT OF MATHEMATICS, EAST CHINA NORMAL UNIveRsITY, LANE 500, DoncCuvan Road, SHANGHAI CiTy, 200241, PEOPLE’s REPUBLIC OF CHINA.

Abstract

In this note we present an application of \(q\)-Lucas theorem, from which the \(q\)-binomial rational root theorem obtained by K. R. Slavin can be deduced as a special case.