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- W3023614906 abstract "It is shown that for any prime $p$ and any natural numbers $ell, m,$ and $s$ such that $0<s<p$, the three following congruences begin{align*}sum_{ige ell+1}(-1)^{m-i} {m choose i}{m+s-1+i(p-1) choose m+s-1+ell(p-1)} &equiv 0 bmod p sum_{ige 0}(-1)^{m-i} {m choose i}{ell+ip choose m+s-1}&equiv 0 bmod p^m sum_{j,ige ell}(-1)^{j-i}{m choose j} {j choose i}{j+s-1+i(p-1) choose j+s-1+ell(p-1)}&equiv 0 bmod p^{m-ell} end{align*} hold true. The corresponding quotients involve Adelberg polynomials which can be computed explicitly, providing closed-form expressions for these sums, valid even if $p$ is not prime, when the congruences do not necessarily hold." @default.
- W3023614906 created "2020-05-13" @default.
- W3023614906 creator A5056418192 @default.
- W3023614906 date "2020-03-29" @default.
- W3023614906 modified "2023-09-27" @default.
- W3023614906 title "Congruences for certain lacunary sums of products of binomial coefficients" @default.
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