Lucas-type Congruences for Cyclotomic Ψ-coefficients
نویسندگان
چکیده
Let p be any prime and a be a positive integer. For l, n ∈ {0, 1, . . . } and r ∈ Z, the normalized cyclotomic ψ-coefficient {n r } l,pa := p − ⌊ n−pa−1−lpa pa−1(p−1) ⌋ ∑ k≡r (mod pa) (−1) (n k )( k−r pa l ) is known to be an integer. In this paper, we show that this coefficient behaves like binomial coefficients and satisfies some Lucas-type congruences. This implies that a congruence of Wan is often optimal, and two conjectures of Sun and Davis are true.
منابع مشابه
Lucas - Type Congruences for Cyclotomic Ψ - Coefficients 3
Let p be any prime and a be a positive integer.
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Let p be any prime and a be a positive integer.
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Let p be any prime and a be a positive integer. := p − n−p a−1 −lp a p a−1 (p−1) k≡r (mod p a) (−1) k n k k−r p a l is known to be an integer. In this paper, we show that this coefficient behaves like binomial coefficients and satisfies some Lucas-type congru-ences. This implies that a congruence of Wan is often optimal, and two conjectures of Sun and Davis are true.
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