query: Divisibility of $\binom{74}{37} -2$ where $\binom{74}{37}$ is a central binomial coefficient
positive_passages.docid: 22962
positive_passages.text: How to show $\binom{2p}{p} \equiv 2\pmod p$?
negative_passages.docid: 120554
negative_passages.text: highest power of prime $p$ dividing $\binom{m+n}{n}$
negative_passages.docid: 157771
negative_passages.text: Nested exponent modulus, $2^{2^{517}} \pmod {23}$
negative_passages.docid: 24053
negative_passages.text: How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
negative_passages.docid: 124890
negative_passages.text: Divisibility within a block of natural numbers
negative_passages.docid: 144571
negative_passages.text: A conjecture including binomial coefficients
negative_passages.docid: 27922
negative_passages.text: prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
negative_passages.docid: 15915
negative_passages.text: For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
negative_passages.docid: 71797
negative_passages.text: Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
negative_passages.docid: 28957
negative_passages.text: Verifying that $2^{44}-1$ is divisible by $89$
negative_passages.docid: 92166
negative_passages.text: Number of odd binomial coefficients is a power of $2$
negative_passages.docid: 66019
negative_passages.text: Revisited: Binomial Theorem: An Inductive Proof
negative_passages.docid: 49234
negative_passages.text: Sum of binomial coefficients with index divisible by 4
negative_passages.docid: 7143
negative_passages.text: Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$
negative_passages.docid: 147496
negative_passages.text: Rules of thumb for divisibility
negative_passages.docid: 97947
negative_passages.text: How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?
negative_passages.docid: 140632
negative_passages.text: A problem on Binomial Theorem