query: Binomial coefficient formula: Why the dividend is a multiple of divisor
positive_passages.docid: 30136
positive_passages.text: Proof that a Combination is an integer
negative_passages.docid: 144814
negative_passages.text: If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?
negative_passages.docid: 82071
negative_passages.text: divisor of a product of integers is a product of divisors
negative_passages.docid: 149759
negative_passages.text: Problem on multiplication formulae.
negative_passages.docid: 125512
negative_passages.text: Doubt regarding divisibility of the expression: $1^{101}+2^{101} \cdot \cdot \cdot +2016^{101}$
negative_passages.docid: 133420
negative_passages.text: Computing the binomial series: $\binom{n}{2}\cdot2^2+\binom{n}{4}\cdot2^4+\binom{n}{6}\cdot2^6+\cdots+ \binom{n}{n}\cdot2^n$
negative_passages.docid: 15666
negative_passages.text: explanation for a combinatorial identity involving the binomial coefficient
negative_passages.docid: 118161
negative_passages.text: Proof of dividing fractional expressions
negative_passages.docid: 57744
negative_passages.text: Strange behaviour of binomial coefficient's delimiters
negative_passages.docid: 116970
negative_passages.text: On the number divisors of a number
negative_passages.docid: 143945
negative_passages.text: Summation of combination of binomial coefficient
negative_passages.docid: 144801
negative_passages.text: $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\dots+\frac{1}{1331}=\frac{p}{q}$; is $p$ divisible by $1997$?
negative_passages.docid: 94060
negative_passages.text: Sum of square binomial coefficients
negative_passages.docid: 114418
negative_passages.text: A deduction from $x^n-1=(x^2-1)\prod_{k=1}^{(n-2)/2}[x^2-2x\cos{\frac{2k\pi}{n}}+1]$
negative_passages.docid: 157417
negative_passages.text: Understanding the definition of a multiple (double) root
negative_passages.docid: 108401
negative_passages.text: Sum of binomial coefficients $\sum_{k=0}^{n}(-1)^k\binom{n}{k}\binom{2n - 2k}{n - 1} = 0$
negative_passages.docid: 40241
negative_passages.text: Understanding the multiplication of fractions