query: Prove that in each year, the 13th day of some month occurs on a Friday
positive_passages.docid: 18094
positive_passages.text: Prove that every year has at least one Friday the 13th
negative_passages.docid: 6595
negative_passages.text: Solve for positive integers: $\frac{4}{13}=\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$
negative_passages.docid: 16660
negative_passages.text: Prove that any positive number has an $n$th root
negative_passages.docid: 129163
negative_passages.text: Showing that every positive integer can be represented in this form
negative_passages.docid: 98514
negative_passages.text: Prove by induction that the number of derangements of length $n$ is $D_n = (n-1)(D_{n-1}+D_{n-2}), n>2$
negative_passages.docid: 76635
negative_passages.text: Proof through combinatorial argument
negative_passages.docid: 106456
negative_passages.text: Identify $P(2014)$ if $P(i)=1/i$ for every positive integer $1\le i\le2013$
negative_passages.docid: 127400
negative_passages.text: Prove that ∀ n ∈ {n | n ∈ ℕ ∧ n > 7}: n = x*3 + y*5
negative_passages.docid: 61483
negative_passages.text: Prove the following identity combinatorially
negative_passages.docid: 53162
negative_passages.text: $13\mid4^{2n+1}+3^{n+2}$
negative_passages.docid: 136562
negative_passages.text: How to get the day of week and the month of the year?
negative_passages.docid: 14480
negative_passages.text: Proving $(P(AB))^2+(P(AB^c))^2+(P(A^cB))^2+(P(A^cB^c))^2\ge\frac{1}{4}$ for any events $A$ and $B$
negative_passages.docid: 79686
negative_passages.text: How can I prove these statements?
negative_passages.docid: 133017
negative_passages.text: Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
negative_passages.docid: 32119
negative_passages.text: Distribution of days in a week on Christmas
negative_passages.docid: 80429
negative_passages.text: probability that exactly two accidents happen in any day of a week if 7 accidents happen in a week
negative_passages.docid: 83736
negative_passages.text: The probability that no person has the same birthday month