2023/04/30 by Yifan Chen, Xiaoxia Wang, Chen, Yifan +1
Mathematics · #11A07 #11B65 #33D15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2305.00396
openalex publication_date 2023/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present several new q-congruences on the q-trinomial coefficients introduced by Andrews and Baxter. As a conclusion, we obtain the following congruence: ( \binomap+bcp+d )≡( \binomac )( \binombd )+( \binomac+1 )( \binombd-p )\pmodp, where a,b,c,d are integers subject to a ≥ 0, 0 ≤ b,d ≤ p-1, and p is an odd prime. Besides, we find that the method can also be used to reprove Pan's Lucas-type congruence for the q-Delannoy numbers.