On binomial coefficients modulo squares of primes

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Grinberg, Darij;
  • Subject: Mathematics - Combinatorics | 11B65, 11A07, 05A10 | Mathematics - Number Theory

We give elementary proofs for the Apagodu-Zeilberger-Stanton-Amdeberhan-Tauraso congruences $$\sum\limits_{n=0}^{p-1}\dbinom{2n}{n} \equiv\eta_{p}\mod p^{2},$$ $$\sum\limits_{n=0}^{rp-1}\dbinom{2n}{n} \equiv\eta_{p}\sum\limits_{n=0}^{r-1}\dbinom {2n}{n}\mod p^{2}$$ and ... View more
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