Some Supercongruences on q-Trinomial Coefficients

The trinomial coefficients n k are given by ∑ k = - n n n k x k = ( 1 + x + x - 1 ) n . Andrews and Baxter listed six kinds of q -trinomial coefficients ( q -analogues of the trinomial coefficients). In this paper, we obtain some supercongruences on these q -trinomial coefficients. As a conclusion,...

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Bibliographic Details
Published inResultate der Mathematik Vol. 78; no. 4; p. 130
Main Authors Ni, He-Xia, Wang, Li-Yuan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2023
Springer Nature B.V
Subjects
Conflicts of interest
Congruences
Mathematical problems
Mathematics
Mathematics and Statistics
Numbers
Theorems
11A07
05A30
Secondary 05A10
cyclotomic polynomial
Primary 11B65
trinomial coefficients
binomial coefficient
Supercongruence
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ISSN1422-6383
1420-9012
DOI10.1007/s00025-023-01913-7

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Summary:The trinomial coefficients n k are given by ∑ k = - n n n k x k = ( 1 + x + x - 1 ) n . Andrews and Baxter listed six kinds of q -trinomial coefficients ( q -analogues of the trinomial coefficients). In this paper, we obtain some supercongruences on these q -trinomial coefficients. As a conclusion, we obtain the following new supercongruence: ap b p ≡ a b ( mod p 2 ) , where a ,  b are positive integers subject to a > b and p > 3 is an odd prime.
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ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-023-01913-7