1. Constant term evaluation and two kinds of congruence.
- Author
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Hou, Qing-Hu and Wang, Yu-Shan
- Subjects
- *
GEOMETRIC congruences , *INTEGERS , *MATHEMATICAL sequences , *PRIME numbers , *BINOMIAL coefficients , *CATALAN numbers - Abstract
We consider two kinds of congruence proposed recently by Sun. The first one is of the form 1 n ( a p n − χ p ⋅ a n ) ≡ 0 ( mod p 2 ) , where p is a prime, χ p is a character and { a n } n ≥ 1 is a sequence of integers. By using a constant term expression for 2 k k , we derive congruence for two sequences { a n } n ≥ 1 . The second one involves the sum S ( a , x ) = ∑ k = 0 p − 1 a k d k ( x ) , where d n ( x ) = ∑ k = 0 n n k x k 2 k. By giving a constant term expression for d n ( x ) , we derive a congruence for S ( a , x ) modulo a prime p. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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