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- W3013522011 abstract "We give elementary proofs for the Apagodu-Zeilberger-Stanton-Amdeberhan-Tauraso congruences $$sumlimits_{n=0}^{p-1}dbinom{2n}{n} equiveta_{p}mod p^{2},$$ $$sumlimits_{n=0}^{rp-1}dbinom{2n}{n} equiveta_{p}sumlimits_{n=0}^{r-1}dbinom {2n}{n}mod p^{2}$$ and $$sumlimits_{n=0}^{rp-1}sumlimits_{m=0}^{sp-1}dbinom{n+m}{m}^{2} equiveta_{p} sumlimits_{m=0}^{r-1}sumlimits_{n=0}^{s-1}dbinom{n+m}{m}^2mod p^2,$$ where $p$ is an odd prime, $r$ and $s$ are nonnegative integers, and $eta_{p}= begin{cases} 0, &text{if }pequiv0mod 3; 1, & text{if }pequiv1mod 3; -1, &text{if }pequiv2mod 3 end{cases}.$$" @default.
- W3013522011 created "2020-04-03" @default.
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- W3013522011 date "2019-01-01" @default.
- W3013522011 modified "2023-09-26" @default.
- W3013522011 title "On Binomial Coefficients Modulo Squares of Primes." @default.
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