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Partial Lucas-type congruences

Partial Lucas-type congruences
Armin Straub — The Ramanujan Journal — dedicated to George Andrews and Bruce Berndt for their 85th birthdays — Volume 69, 2026, Pages 1-14

Abstract

In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes \(p\) satisfies congruences that are analogous to Lucas' theorem for the binomial coefficients with the notable twist that there is a restriction on the \(p\)-adic digits. We prove a general result that shows that similar partial Lucas congruences are satisfied by all sequences representable as the constant terms of the powers of a multivariate Laurent polynomial.

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BibTeX

@article{partial-lucas-2026,
    author = {Armin Straub},
    title = {Partial Lucas-type congruences},
    journal = {The Ramanujan Journal},
    year = {2026},
    volume = {69},
    pages = {1--14},
    doi = {10.1007/s11139-025-01275-4},
}